The major parallel architecture classes are considered: single-instruction multiple-data (SIMD) computers, tightly coupled multiple-instruction multiple-data (MIMD) computers, hypercuboid computers and constant-valence MIMD computers. An argument that the PRAM model is universal over tightly coupled and hypercube systems, but not over constant-valence-topology, loosely coupled-system is reviewed, showing precisely how the PRAM model is too powerful to permit broad universality. Ways in which a model of computation can be restricted to become universal over less powerful architectures are discussed. The Bird-Meertens formalism (R.S. Bird, 1989), is introduced and it is shown how it is used to express computations in a compact way. It is also shown that the Bird-Meertens formalism is universal over all four architecture classes and that nontrivial restrictions of functional programming languages exist that can be efficiently executed on disparate architectures. The use of the Bird-Meertens formalism as the basis for a programming language is discussed, and it is shown that it is expressive enough to be used for general programming. Other models and programming languages with architecture-independent properties are reviewed. >