We do not have a specific "object follow" mode for animation but you can pick an "orbit point" in the 3D preview which will help you keyframe such a motion. Use the button that is 2nd from the right on the toolbar at the bottom of the 3D preview - it looks like a small cross-hair/target indicator. The mouse-over tooltip should make it clear. Once your "orbit point" is selected, you will need to manually set keyframes as you move the camera around this point and adjust frame position as well.
- Oshyan