Infinite games are a strong model for analyzing dynamic networks that encounter continuous topological changes during operation. In this framework, the players represent the contrary forces which modify the network. This dissertation deals with three different two-player games which focus on guaranteeing routing and connectivity properties in dynamic networks. In each model, one player has to establish the proper operation of the network, while the adversary produces failures and demands that occur during operation.In the first part, sabotage games (van Benthem, 2002) are studied. In these games, a Runner traverses a graph and tries to reach a set of goal vertices, while a Blocker removes edges. In the second part, routing games are developed in which a routing agent has to deliver packets to their destinations, while a demand agent continuously generates packets and blocks connections for a certain amount of time. In the third part, connectivity games between a Constructor and a Destructor are introduced. While Destructor deletes nodes, Constructor can restore or even create new nodes under certain conditions. Constructor"s objective is to either establish a connected network or guarantee that the network always stays connected.