We take a historical approach to our presentation of self-scheduled task parallelism, a programming model with its origins in early irregular and nondeterministic computations encountered in automated theorem proving and logic programming. We show how an extremely simple task model has evolved into a system, asynchronous dynamic load balancing (ADLB), and a scalable implementation capable of supporting sophisticated applications on today’s (and tomorrow’s) largest supercomputers; and we illustrate the use of ADLB with a Green’s function Monte Carlo application, a modern, mature nuclear physics code in production use. Our lesson is that by surrendering a certain amount of generality and thus applicability, a minimal programming model (in terms of its basic concepts and the size of its application programmer interface) can achieve extreme scalability without introducing complexity.