We present an overview of different actor oriented models of network evolution, that have been developed in the last couple of years. The models are constructed in different fields of application and all have in common that the emergence of network structure is directly or indirectly of interest. Each model is based on a set of actors and a set of behavioral rules of these actors, resulting in interaction mechanisms and the coming into existence of some network pattern of relationships. Actors vary from individuals and families to political parties. Relationships are either directed or undirected and vary from friendship to cooperation, and access to coalition partners. Simulation is used to obtain distribution of possible resulting network structure because this and other aspects of the models, make it hard to be solved analytically. We think that the use of this kind of simulation models, by examining the influence of both endogeneous and exogeneous variables, contributes to improvement of theory building.