The complex problem of assigning tasks to processing elements in order to optimize a performance measure has resulted in numerous heuristics aimed at approximating an optimal solution. This article addresses the task scheduling problem in many of its variations and surveys the major solutions. The scheduling techniques we discuss might be used by a compiler writer to optimize the code that comes out of a parallelizing compiler. The compiler would produce grains of sequential code, and the optimizer would schedule these grains such that the program runs in the shortest time.