In this thesis constraint solving/satisfaction is presented as a model of computation. Advantages of using constraints as a paradigm of programming are presented. A semantic schema for constraint based computations is given, following a brief survey of the more important systems based on constraints. These systems range from particular algorithms to problem solvers to constraint based general purpose programming languages. Finally, constraint satisfaction is applied to logic programming and theorem proving. It is shown that incorporating constraint solving in definite clause programs enhances their expressive power. Also, an alternative semantics - based on constraint satisfaction - is given for theorem proving.