Do the 70-200mm AF on my Nikon D5100 camera?

I have the Nikon D5100, but i notice not all lens AUTO focus with the camera? I want to buy the 70-200mm lens. How do I know if it auto focus with my camera?
~Also are sigma lens good? Same question ^

You need to check if the lens has an auto focus motor in it, it will generally say it does. For example, the Sigma 70-200mm F/2.8 HSM has an auto focus motor in the lens so it will work with the D5100. If you specified the make and model of 70-200mm lens we could help more.

And yes, Sigma lenses are great when you get a good copy of one. They have a big problem with quality control though so you may have to return a lens for another version if you buy from them, but that's not too bad. They're affordable and many many people use them, recently I worked with a professional wedding photographer who shot with a Canon 5D Mark III and Sigma 85mm F/1.4.

Opinion is divided, but Sigma produce some nice lenses. Look for individual reviews.

Nikkor lenses which work with your camera are AF- S, Sigma lenses are HSM.

More than likely yes… Sigma lenses are pretty hit-or-miss.