How can I have the camera track an object mid animation

I have an object that I have fly towards the camera. I want to start the shot with the camera not following the object but then I want it to lock onto it as it gets closer and follow it through the rest of the animation. How would I accomplish this? Thanks.

You can add a Track To constraint to the camera and specify the object to follow in the constraint properties. And then animate the influence of the constraint when needed.