String networks with Y-junctions, at which 3 different strings meet, may be found in a number of different situations. An example is a network of (p,q) strings thought to be formed at the end of brane inflation. We discuss both local and global aspects of networks with Y-junctions, with the eventual aim of determining their cosmological consequences. In particular, we examine the process of intercommutation in which 2 strings collide and exchange partners becoming joined by a third string. We show that there are important kinematical constraints on such a process, depending on the relative velocity, orientation and tension of the two initial strings. The potential consequences of these constraints on network evolution are discussed. We then determine some of the global properties of the network, such as the mean velocity of the Y-junctions. We show that the evolution of the network may be such as to preferentially remove the heaviest strings, and we discuss how this result is consistent with studies of string statistical mechanics.