Flash Photography has been around since nearly the beginning of phtography (which included a New Zealander making early telephoto lenses in the 1880s, and learning about types of lens abberations).

In the beginning flash photography involved igniting chemicals, and these gradually became more automated and modularised. Because chemicals take a while to ignite, and produce non-trivial amounts of light, flash synchronisation involved setting off the flash substantially before opening the shutter, in order that the scene was lit up when the shutter was open (rather than well after it closed). Different technologies took different amounts of time to reach a useful level of light, which led to M-sync setting the flash off 20ms before opening the shutter and F-sync setting the flash off 5ms before opening the shutter. Modern camera flash uses Xenon flash tubes, which take very little time (well under 1ms) to activate -- because they are triggered via pre-charged capacitors (DIY information). To deal with this (comparatively rapid) speed, X-sync fires the flash once the shutter is fully open.

Because the light from the Xenon flash tube starts and ends so quickly (less than 1ms), there is a (camera-dependant) limit to the maximum shutter speed that can be used with a single flash from a Xenon flash tube, called the maximum X-sync speed. If one tried to exceed that speed (and modern cameras contain software interlocks prohibiting doing so in any automated flash mode), then the flash would fire when only some of the sensor (or film) was exposed, so some portions of the frame would be properly exposed and other parts would be (massively) underexposed.

The maximum X-sync speed for a given camera depends on the shutter technology. Cameras with interchangeable lenses, such as SLR (Single Lens Reflex) cameras, typically use focal plane shutters, which have two "curtains" in front of the sensor (or film) that are pulled across so as to leave a gap between them that determines the time of the exposure. The advantage here is that the shutter stays with the sensor (camera body), and so only one is needed for the camera system (and thus the lenses can be cheaper). Other options include leaf shutters, and central shutters both of which open "all at once", but because they are "all at once" have mechanical limits on how fast they can move that apply to all photographs taken with them (not just flash photographs); by contrast focal plane shutters can surpass these mechanical limits for non-flash photography by exploiting the difference in the start time of the movement of the two curtains so that only a portion of the frame is exposed at any point in the exposure, thus achieving a faster effective exposure time. (Digital cameras also have the option of an electronic shutter -- ie resetting the sensor and collecting light for a short period of time -- which offers the possibility of faster shutter speeds that are not limited by mechanical movement, but this is not widely deployed in SLRs except at the very high end.)

The maximum X-sync speeds for focal plane shutters generally range from 1/60th of a second (approx 17ms) in old SLRs to 1/300th of a second (approx 3ms), depending on the size of the frame (larger frame means more distance to cover) and the speed at which the shutter curtains can move. (Table of Canon EOS camera maximum X-sync speeds; low end Canon Digital SLRs, including mine, are 1/200th of a second (5ms).) The maximum movement speed is dictated by mechanical considerations including being able to accurately start/stop the shutter curtains, without introducing unwanted vibration. Leaf shutters and central shutters can normally offer maximum X-sync speeds from 1/125th of a second (8ms) to 1/500th of a second (2ms) (and that speed is usually also their maximum shutter speed); combining a focal plane shutter with an electronic shutter also allows achieving a maximum X-sync speed of 1/500th of a second (2ms) and this is offered on high end SLRs.

Since there is often a desire to use a fast shutter speed to be able to hand-hold the camera during the shot, and minimise motion blur, the relatively low (by modern standards) maximum X-sync speeds in most SLRs (with focal plane shutters) can be inconvenient when using flash. To work around this, higher end flash units (eg, typical "off camera" flashes from the camera vendor) also support a flash mode that can be safely used with a faster shutter speed, called "High Speed Sync" or FP-sync (Focal Plane). This mode works by pulsing the flash at high speeds, effectively sharing the flash charge/light over the whole period of time that the focal plane shutter takes to cover the sensor. Since this effectively stretches the flash from (less than) 1ms to the total exposure time it can be used with any shutter speed. However because the light is being shared over multiple flash pulses, the amount of light in each pulse is much reduced and thus the range of the flash is much reduced (less than 1/4 of the distance is common). This normally isn't a problem when using flash for fill-in lighting.

However there is often a desire to use a fast shutter speed to stop motion, and the FP-sync mode does not work for this, since freezing motion needs a single pulse of light (or properly spaced for the motion set of pulses). To stop really fast motion (eg, projectiles) people have experimented with making air gap flashes, which use a very high voltage to discharge a very short duration spark in air. This leads to some amazing stopped motion photographs (found via comments on Clarisse Thorne's open thread post). To avoid completely missing the action it's necessary to trigger the shutter and flash automatically, using something like a CameraAxe, as shown here (the CameraAxe is an open hardware project with a Creative Commons license, but also available pre-assembled). At these speeds shutter lag can be a major problem, and most people take these very high speed photos in a dark room with a relatively long shutter time (to ensure the shutter is completely open when the action happens) and the CameraAxe triggering the flash to illuminate, and stop, the motion.

Back at more human speeds, with shutter speeds under the maximum X-sync time (and thus longer than a single 1ms flash pulse), there is still an opportunity to "stop" motion, by triggering the flash towards the end of the exposure. This is called "rear curtain sync" or "2nd curtain sync", and results in motion blur leading up to a final well defined image which works well to show people or human-speed objects in motion. However the default is "1st curtain sync", where the flash is fired as soon as the sensor (or film) is fully uncovered, which leads to the opposite effect (motion blur after the well defined image, so that it appears to be moving backwards). This "1st curtain sync" default is chosen because automated flash needs a short flash pulse to determine the correct amount of flash light required -- by measuring the light levels reflected back -- and if the main flash pulse is at the start of the exposure then the "measuring pulse" and the main flash pulse occur together which minimises the risk of, eg, people blinking or looking away thinking the photo has been taken (by contrast with "2nd curtain sync" the measuring pulse happens just before the exposure and then there is a delay before the main flash pulse). On a Canon EOS 550D camera, "2nd curtain sync" can be set on both the internal flash and on a compatible external flash: Menu, bottom of first page ("Camera"), Flash Control, Built-in flash func. (or external flash, as appropriate), Shutter Sync, Second Curtain (and "1st curtain sync" can be reset in the same location).

Modern external flashes connect via a hot shoe (which has been standardised as ISO 518:2006), which at minimum have an outer metal shoe and a central metal pin: the flash is triggered by shorting the central pin to the metal shoe. (Camera accessory shoes date back to the 1930s, and were originally used with accessory viewfinders with the flash being triggered by a Prontor-Compur (PC) socket and cable; the use of hot shoes dates to about the 1960s, and on modern 21st century camera only some high end cameras still have PC sockets, for compatibility with older studio flashes, but a "universal translator" will convert a hot shoe signal to a PC socket, and a Wein adapter can add a PC connector to any flash.) Because of this "short the contacts" approach to triggering the flash, one needs to be aware of the trigger voltage used by the flash: older flashes could short the entire flashtube trigger voltage (often 300V or more) via the camera hot shoe connectors, potentially causing damage to modern cameras (which expect only about 6V, connected to an indicative "pulled up, active low" line).

The ISO hot shoe standard only covers basic flash communication -- essentially "make light now" -- with everything else configured manually on the flash unit (and the camera to match). In order to make the process more automated (and allow on-camera configuration of the flash settings, even when using an external flash) most camera vendors include additional communication pins on the hot shoe that allow more precise control of their models of flash with their cameras. Canon includes four additional pins in their modern (E-TTL and E-TTL II) flashes. (Prior to E-TTL, introduced in 1997, Canon used TTL (Through-The-Lens) metering which measured flash light reflected off the film during the flash -- a significant improvement on a fully manual flash where the flash itself tried to guess when enough light had been emitted with no help from the camera; there was also an Advanced-TTL (A-TTL) for some combinations of Canon camera and flash which added a pre-flash to help with flash metering, using the same in-camera sensor measuring light reflected off the film. Only E-TTL and E-TTL II flashes will work, in anything other than fully manual mode, with Digital SLRs -- since DSLRs have no film off which the light could reflect!)

Other than the automation of the flash, another important characteristic of flashes is their maximum light output power, which is described by the Guide Number (light less than the maximum is achieved either by reducing the charge in the flash or by cutting off the duration the flash is triggered, or both). By convention the Guide Number is the distance that can be illuminated by the flash for a proper exposure with ISO 100 (film/sensor) speed and a f/1.0 aperture: typically measured in metres, but sometimes measured in feet (particularly in the USA) so one needs to confirm the units used. At a faster sensor speeds (ISO number), the guide number can be scaled by sqrt(2) (1.4) for each doubling of the ISO number; for smaller apertures the distance is scaled down by the number of stops reduced from f/1.0. The built-in flash on, eg, the Canon EOS 550D has a Guide Number of 13, so will cover up to 13 metres at ISO 100 in the unlikely event it is paired with a f/1.0 lens and aperture (and less distance at smaller apertures give or take the ability to use a faster sensor ISO).

Canon's external flash units are numbered based on the maximum Guide Number they can achieve, multiplied by 10; the suffix then indicates the capabilities of the flash unit (an "EX" or "EX II" suffix indicates that it supports E-TTL or E-TTL II respectively, and thus can be used with a Canon Digital SLR; an "EZ" suffix indicates it has a zooming head and supports TTL/A-TTL which only works automatically with film cameras; most "EX" external flashes also have zooming heads). In flashes with zooming heads, the flash unit is able to move the flash reflector to focus the light in the area where it is most needed, which enables them to achieve suitable flash coverage at a longer distance, while still preserving wide angle coverage, without needing to increase the flash tube light output. The Canon Speedlite 430EX (II) and Canon Speedlite 580EX (II) have zooming headers; the entry level Speedlite 220EX and Speedlite 270EX do not (sadly the Speedlite 270EX doesn't even have an IR (infrared) focusing lamp, unlike the older Speedlite 220EX). For this reason the Canon Speedlite 430EX II is probably the smallest Canon external flash worth purchasing for a modern Canon Digital SLR.

PhotoNotes have an excellent guide to Flash with Canon EOS cameras (and have literally "written the book" on Canon EOS Camera flash use). It's particularly important to note the different ways the camera will treat flash in the different camera modes (cf on Canon Powershot G cameras). Roie Galitz has a good introduction to flash photography. And Toomas Tamm has written a good guide to Flash, as does Bob Atkins.

The Strobist Blog has two awesome introductory series on Lighting: 101 and 102, as well as "a look at Monoblocs": Part 1 and Part 2. Studio lighting is a specialist area, which is best done with less portable (than camera-mountable) lighting units (of which a "monobloc" is one type of studio-only light), and special techniques, but otherwise relatively inexpensive compared with trying to collect camera-mountable flashes and trigger them together.

ETA, 2011-06-14: Bob Atkins guide to Canon Flashes, but note that there are two newly released ones which seem to be aimed at the entry level/digital video market. (Also Canon Speedlite 430EX II review.)