A lighting system with removable light modules mounted on a frame by an attractive force between magnetic material of the light module and magnetic material of the frame such that a light module may be installed on, removed from, or relocated on the frame manually without tools or permanent electrical connection. The frame may be one-, two-, or three-dimensional, and it may provide an aesthetic appearance even when the lighting system is not illuminated. The light modules may employ incandescent, quartz-halogen, LED, or fluorescent light sources. Particularly, in LED embodiments, the magnetic materials serve the dual functions of mounting and heat sinking. The lighting system may be utilized as a sign, signaling device, or a building block in larger lighting systems. The lighting system has a wide variety of applications and provides a user with improved ability to control the quantity, direction, and characteristics of the emitted light.