Handheld camera work is a method of shooting that is often used in almost all movies that are shot today. Its a very popular trend usually meant to evoke a sense of realism and the feeling that the camera is the viewer looking into the action.
I always feel like there is a time and a place for handheld work since it is a style and a choice. Whenever a director says we are going handheld, I constantly question what the motivation is for handheld. When there is a proper motivation for handheld work it can be incredibly powerful and do great things for a scene.
Doing handheld "right" though, is something that is a bit subjective as everyones definition of handheld varies slightly. Also with handheld your lens selection becomes a little less large, but thats one of the trade offs of this style. The biggest thing to keep in mind though is where your action is taking place and to keep in mind where you are moving, since you as a camera operator dictate where the 180 lands when doing handheld. So be mindful, so you can match your shots right in coverage.
Here is a great video by Sean Bobbitt, BSC, teaching a little master session on handheld camera work. For those of you unfamiliar with his work, check out his impressive IMDB and his newest "12 Years a Slave".
Head to the 8 min mark to skip the ARRI intro. (Some good info on Anamorphics in that intro though)