How do children learn to read? How do deficits in various components of the reading network affect learning outcomes? How does remediating one or several components change reading performance? In this article, we summarize what is known about learning to read and how this can be formalized in a developmentally plausible computational model of reading acquisition. The model is used to understand normal and impaired reading development (dyslexia). In particular, we show that it is possible to simulate individual learning trajectories and intervention outcomes on the basis of three component skills: orthography, phonology, and vocabulary. We therefore advocate a multifactorial computational approach to understanding reading that has practical implications for dyslexia and intervention.