Although progress has been made in optical interconnections, electrical interconnections continue to dominate most of the hierarchical interconnect layers that comprise computer systems. (The delay in the industry's move to optics is largely due to the continued improvements in electrical links, most notably the addition of equalization schemes [1].) The challenges faced by electrical interconnections [2] are described along with a presentation of the potential benefits optical interconnections afford. Commercial success for optical interconnections has largely been in rack‐to‐rack links, where the distances are great enough to require the low loss advantages of optical transmission. Further work on optical schemes for each layer of interconnection hierarchy, rack to rack, board to board, and intraboard is presented. These schemes can be broken into two general types of guided wave solutions that use fibers or waveguides as transmission media and free‐space solutions, which require only the optical elements. Advantages and examples of links using each type are described. It is shown that free‐space optical interconnections board to board can reduce wiring congestion dramatically over electrical or guided wave approaches, which force all interconnections to pass between the boards through the backplane. The density achievable can be further improved by employing 3D interconnection arrangements which are discussed in the intraboard examples. Optical interconnection will gradually penetrate from the outer levels of the systems to the inner as the technology matures, but all of these interesting possibilities will remain possibilities unless future areas of study include focus on low cost, small size for high density and high reliability of optical interconnections and devices.