In the past century, combinatorial designs have had substantial application in the statistical design of experiments and in the theory of error-correcting codes. Applications in experimental and theoretical computer science have emerged more recently, along with connections to the theory of cryptographic communication. This paper focuses on applications of designs in multiple access communications, in particular to balanced methods of sharing resources such as communications hardware, time, and bandwidth. The theory of combinatorial designs continues to grow, in part as a consequence of the variety of these applications and the increasing depth of the connections with challenging problems on designs.