In illustrative implementations of this invention, a human user mechanically moves one or more moveable parts in a handheld controller, and thereby optically controls a mobile computing device. In illustrative implementations, the optical control is implemented as follows: A camera onboard the mobile computing device captures images. The images show the motion of the moveable parts in the handheld controller. A camera onboard the mobile computing device analyzes these images to detect the motion, maps the motion to a control signal, and outputs a control signal that controls a feature or operation of the mobile computing device.