One part of video that is very different from still photography is choice of shutter speed. With still photography, you can choose any shutter speed your camera offers, selecting fast shutter speeds to stop action, slow shutter speeds to give interesting blurs, and all shutter speeds to balance a needed f-stop chosen for depth of field. Unfortunately, you cannot do that with video.
First, you are limited on the slow side. Video is typically shot at 24-30 frames per second. Essentially that means you cannot shoot slower than 1/30 second because you cannot shoot that many frames per second if you could (e.g., you could only shoot 20 frames per second if you shot at 1/20 sec -- 20 x 1/20 = 1). That is a definite limit.
Second, you are limited on the fast side. It is possible to shoot video at very fast shutter speeds, but the video won't look right. Think of it this way -- if you shot 30 fps at 1/1000, you would actually be exposing 30/1000 of that second. That would mean that 970/1000 of that second would not be recorded. The result is very visible "gaps" in the action so that the image looks jerky and jumpy when it is played back. It does not look like normal video. For this bee video, all of the bees flying around would look very odd, with jerky, interrupted flight. (On the other hand, if you were shooting in order to be able to freeze action and look at the details (such as analyzing a golf swing), then the high shutter speed would work.)
The best shutter speeds for video range from 1/30-1/125 (although with very fast action, even 1/125 can start to look jerky). Some videographers say the best speed is approximately two times the frames per second, such as 1/60 for 30 fps. I use 1/30-1/125 all the time without problems.
So what do you do if the light level falls? There is no other option for normal video than to shoot with higher ISO settings because you aren't going slower than 1/30 sec. What happens if the light gets bright? You have to stop your lens down. What if you can't stop down enough or you want to use a wider f-stop? Obviously, you need to use the slowest ISO possible, but then you need a neutral density filter (a polarizing filter can help to a degree, too).
A neutral density filter is an important filter for video because it gives you more options for exposure. It also lets you really gain a great benefit of using a DSLR for video -- the ability to control depth of field to very narrow amounts. This was not readily possible with most commonly available camcorders. Because they used such a small sensor, they also used very short focal lengths for lenses. That caused a lot of apparent depth of field, no matter what you did. It was hard to shoot selective focus. But with an ND filter, you can cut the light on a longer focal length lens on a DSLR (for the same angle of view) and use a wide f-stop for really nice selective focus effects.