Problem solving involves search. In AI we try to find ways of avoiding or minimizing search. An effective approach is to exploit knowledge of the problem domain. Such knowledge often takes the form of a set of constraints. In general, a constraint represents a required relationship among some variables. For this reason we usually assume the existence of some machinery that can enforce a given set of constraints and resolve the conflicts that arise when these are violated. Programming systems based on constraints have been successfully applied to circuit analysis, design and simulation, scene analysis, plan generation, hardware diagnosis and qualitative reasoning. This thesis presents ICONStraint, a programming language based on the constraints paradigm of computation and gives a characterization of consistency conditions and the operations for ensuring consistency in constraint networks designed in the language. In ICONStraint we represent constraint systems in dependency structures and use reason maintenance, local propagation and dependency directed backtracking for computation and consistency maintenance. ICONStraint has been implemented in Interlisp-D.