Do push ups work for your biceps?

Yes and no.

Biceps are used for pulling motions that bend your elbow, such as "curl" lifts, tug-of-war, hugging, and drinking a glass of water. They aren't terribly helpful for pushing motions, like push-ups, patty-cake, punching your pillow, or break-dancing; your triceps (not biceps) are the primary upper-arm muscles used in these activities.

But there's more to it than that.

In order to have bulging biceps, you will also need to train your triceps. In order to have strong triceps (which are used in push-ups), you will need to develop your biceps. These muscle groups work opposite each other, and you will have an unbalanced system if you try to do one without the other.

Imagine someone with massive, bulging biceps, but very weak and tiny triceps; not only would this person look pretty silly, but they might not even be capable of straightening their arm all the way, because of the constant tension created by the muscle tone of the well-developed biceps (this is also the reason why full range of motion should be used during all muscle-building exercises).

In short, push-ups do not directly do much for your biceps because they are not the primary muscles used in that activity, but they do help build your triceps, which as we learned from the system balance described above, assists in the proper development of the upper arms, including the biceps (but you will also need a different exercise, such as chin-ups or preacher curls, to take advantage of any help that push-ups may have offered the biceps).