Does modeling matter? We address this question by providing a broad survey of the computational models of cognitive development that have been proposed and studied over the last three decades. We begin by noting the advantages and limitations of computational models. We then describe four key dimensions across which models of development can be organized and classified. With this taxonomy in hand, we focus on how the modeling enterprise has evolved over time. In particular, we separate the timeline into three overlapping historical waves and highlight how each wave of models has not only been shaped by developmental theory and behavioral research, but in return also provided valuable insights and innovations to the study of cognitive development. (Contains 3 figures and 2 tables.)