A critical element in building parallel computers that use very fast processing elements is interprocessor communication. To utilize the processing elements efficiently, the interconnects in such parallel computers must provide high data rates and low latencies with extremely high reliability, compactness, and reasonable cost. We discuss the application of free-space optical links for interprocessor communication in parallel computers. Free-space transmitter and receiver modules have been fabricated and installed in a card cage enclosure. Repeatable signal levels have been achieved, after board removal and replacement, without the use of any micropositioners or adjustments. A time-division-multiplexed (TDM) ring network using high-speed (1 Gbit/s), point-to-point, free-space links has been designed to provide full connectivity among a set of processors connected to the ring nodes. Work is under way to demonstrate the 1DM ring network concept in a multiprocessor computer.