All normal humans have the same basic cognitive capacity for language. Nevertheless, the world's languages differ in the kind and number of grammatical options they give their speakers to express themselves with. Sometimes, a language's grammatical constructions may differ in how easy they are for comprehenders to process or how readily speakers will choose them. It has been observed that languages which allow more difficult constructions also tend to allow easier ones, and when a language only allows one option, it tends to allow the easiest to process. This correlation is intuitive: languages tend to give their speakers options that they find easy to use. However, the causal process that underlies it is not well understood. How did the world's languages come to have this convenient property? In this dissertation, I discuss a family of evolutionary models of language change in which processing-efficient variants tend to be selected more frequently, and hence over time have the potential to displace less efficient variants, pushing them out of the language. I begin by showing that a psycholinguistic theory, dependency length minimization, accounts for word ordering preferences in data taken from Old and Middle English just as it does in Present Day English. I then discuss computer simulations of a model of language change which implements this bias, predicting observed word order changes in English. Finally, I present experimental studies of online comprehension in Japanese which not only display evidence for the dependency length bias, but also suggest that comprehenders encode it as part of their knowledge about language, using it to help understand the sentences they receive from their peers.