Brane inflation provides a natural dynamical model for the physics which underlie the inflationary paradigm. Besides their inflationary predictions, brane models imply another observable consequence: cosmic strings. In this dissertation I outline the background of how cosmic strings arise in brane inflationary models and how the properties of the strings and the models are mutually tied (Chapter 2). I then use cosmological observations to put limits on the properties of any actually-existing cosmic string network (Chapter 3). Next, I study the question of how cosmic superstrings, as the cosmic strings arising from string theory are known, could be distinct from classical gauge-theory cosmic strings. In particular, I propose an analytical model for the cosmological evolution of a network of binding cosmic strings (Chapter 4); I also describe the distinctive gravitational lensing phenomena that arecaused by binding strings (Chapter 5). Finally, I lay out the background for the numerical study of a gauge theory model forthe dynamics of cosmic superstring binding (Chapter 6).