This chapter introduces the notion of trust as a means to establish security in mobile ubiquitous applications. It argues that trust is an essential requirement to enable security in open network environments. In particular in wireless ad hoc environments where there is no network topology. In such environments communication can only be achieved via routes that have to be trusted. In general it may be hard, or even impossible, to establish, recall and maintain trust relationships. It is therefore important to understand the limitations of such environments and to find mechanisms that may support trust either explicitly or implicitly. We consider several models that can be used to enable trust in such environments, based on economic, insurance, information flow and evolutionary paradigms.