In this chapter, we introduce an additional, yet essential, concept in describing software architectures : architecture constraints. We explain the precise role of these entities and their importance in object-oriented, component-based or service-oriented software engi-neering. We then describe the way in which they are specified and interpreted. An architect can define architecture constraints and then associate them to architectural descriptions to limit their structure, and for ultimately making persistent a certain level of quality. These constraints enable us to enforce adherence to a particular architecture pattern or style so as to ensure a certain level of maintainability. By interpreting these constraints, we are able to check whether these patterns/styles are respected, after the evolution of architecture descriptions. We present a state of the art on the current techniques and languages for ex-pressing these constraints. We then introduce our recent research, where we have developed languages for expressing these constraints on architectures of object-oriented, component-based and service-oriented applications. We will use different examples of architecture constraints representing known patterns and styles, like the Pipe and Filter architecture style and the Service Facade or Model-View-Controller architecture patterns, to illustrate these works. We conclude this chapter with a summary of some of the open questions which have given rise to ongoing research about this concept of architecture constraints.