For most of human history, our ability to perceive and understand very fast optical events has been limited by the temporal resolution of the human eye. Things that happened too fast were a blur, and all we had to go on was guesswork. Take, for instance, this 1821 painting of a horse race:
If it looks a little bizarre, it's because it guesses wrong on the character of one of those very short events - in this case, the position of a horse's feet during a gallop. Not until the invention of high-speed photography later on in the 19th century could the gallop be better resolved and understood. As it turns out, there is a point in the stride where the horse is entirely out of contact with the ground, but it's the point where all the hooves are brought inward. During the extension of the hooves, one is always in contact with the ground:
(Both images from the Wikipedia horse gait article)
Time went on and science discovered and used faster and faster events, and the technology has had to keep pace. The overall procedure is to find an even faster event than the one you're trying to measure, and use it as part of your examination. In the case of the horse, the faster event is the flash and shutter speed of the camera. This sort of thing can get you down to events as small as a fraction of a millisecond with standard cameras, and specifically designed high-speed cameras can do a bit better. Much below the millisecond range though, and shutters simply can't move fast enough to provide that faster event. Photodiodes can respond much more quickly than film and shutters, and using those along with careful and sensitive measurement it's possible to measure flashes of light with nanosecond resolution. Using streak cameras which trade off spatial resolution for temporal resolution can improve this to resolution of a couple of picoseconds. (The one in our lab can get to about the 1ps range. State-of-the-art can improve on this by perhaps a factor of 10, though at the cost of massive expense for not so much experimental value).
A picosecond is a trillionth of a second, by the way. It's very fast - light only moves around a third of a millimeter in a picosecond - but lots of atomic processes happen much faster. We can both use and study these processes with pulsed lasers, which today can easily reach pulse lengths of a few femtoseconds. A femtosecond is a thousandth of a picosecond, so it's pretty much an unbelievably small amount of time. A sort of typical way of thinking about the orders of magnitude is to note that the speed of light is 300 nanometers per femtosecond, and an average atom might be a few tenths of a nanometer in diameter. These femtosecond pulses are close to the shortest optical events we can currently produce. We'd like to measure them, but remember how we need that shorter (or at least comparably short) event? We just haven't got any laying around, and if we did we'd be studying them which would put us right back at square one.
But we can cheat. What if we could use the pulse itself as that short event? What we do is split the pulse into two copies of itself with a beam splitter. Then we make one pulse travel a slightly longer path to the detector, and by varying that path length the crests and troughs of the two pulses will interfere with each other in a way that depends on the path length difference. This is all detected on a photodiode or photomultiplier or equivalent with only nanosecond resolution and so all we see is a total integrated intensity as a function of path length difference, but we can still extract information from that:
This image is also from Wikipedia. M1 is the movable mirror, and SHG is a nonlinear crystal that responds to the square of the intensity, which allows us a bit more information.
In a way it's like examining the rainfall in a region by looking at a rain gauge once per month. You have no idea if it's been sprinkling all month or if you just had a short but intense cloudburst. In meteorology you'd not be able to say all that much about the day-by-day rainfall by looking at the bucket, but in optics our job is easier because the variable path length gives us a way to tease more information out of the intensity.
What does an autocorrelation look like? Here's one fresh from our lab. It's just a calibration test with standard equipment, so I'm afraid you won't be able to use it to scoop us on our hopefully interesting upcoming results. ;)
Y-axis intensity (au), x-axis femtoseconds. From it, we can say the pulse is about 9 fs long and a little bit messy - the wings indicate the pulse isn't quite a perfect sech^2 shape as we might like. But it's pretty neat that we can so easily measure such a short event with a procedure that's relatively simple and fits in a box not much bigger than one you get a Big Mac in.
You should check out Paul Corkum's work with the National Research Council of Canada in Ottawa on attosecond laser spectroscopy. He's managed to image the wavefunction (not the probability density) of a nitrogen atom and is hoping to essentially film chemistry happening.
Shutters don't have to be mechanical. Wikipedia says that the shutters on the EG&G Rapatronic cameras can have exposure times as short as 10 nanoseconds.
This camera is famous for its stop-action photos of nuclear explosions. Here's a site with some of those images. It says that the average exposure was 3 microseconds.
Before Eadward Muybridge used photography to "stop action", A.M. Worthington used sparks (and persistance of vision) to draw the splash of mercury dropping onto a glass plate, with illumination durations much less than a millisecond.
In "A Study of Splashes" 1908, when he had moved to photography, he used discharges from Leyden jars, noting that the collapse of the magnetic field in an induction coil was too slow.
Other "shutters" can be even faster. Intensified CCDs, for example, can go below a nanosecond (I'm not up on the current limit, but I've seen 200 ps.