[Truncated abstract] Parallel computing is recognised today as an important tool in the solution of a wide variety of computationally intensive problems, problems which were previously considered intractable. While it offers the promise of vastly increased performance, parallel computing introduces additional complexities which are not encountered with sequential processing. One of these is the scheduling problem, in which the individual tasks comprising a parallel program are scheduled onto the processors comprising the parallel architecture. The objective is to minimise execution time while still preserving the precedence relations between the tasks. Scheduling is of vital importance since a poor task schedule can undo any potential gains from the parallelism present in the application. Inappropriate scheduling can result in the hardware being used inefficiently, or worse, the program could run slower in parallel than on a single processor. The scheduling problem is one of the more difficult problems facing the parallel programmer. In fact, it is NP-complete in the general case. As a result, a large number of heuristic methods with sub-optimal performance but polynomial, rather than exponential, time complexity have been proposed. In order to simplify their algorithms, researchers have restricted the problem: by making assumptions concerning the parallel architecture or imposing limitations on the task graph representing the parallel program. The evolution of the task scheduling problem has involved the gradual relaxation of these restrictions. A major change occurred when the assumption of zero inter-processor communication costs was removed. This was driven by the increasing popularity of distributed-memory message-passing multiprocessors.