In modern shared-memory multiprocessors, processes can be halted or delayed without warning by interrupts, preemption, or cache misses. In such environments, it is desirable to design synchronization protocols that are wait-free: any processes that continues to run will finish the protocol in a fixed number of steps, regardless of delays or failures by other processes. Models and techniques borrowed from classical Algebraic Topology have recently yielded a variety of new results for wait-free distributed computing. This talk will survey the basic concepts underlying this approach, and will show how they apply to a simple distributed problem. This talk is self-contained, and is intended for a general audience.