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 chapter, we summarize what we know about learning-to-read and how previous computational models have tackled this issue. We then present our developmentally plausible computational model of reading acquisition and show how it helps to understand both 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. The work advocates a multi-factorial computational approach of understanding reading that has practical implications for dyslexia and intervention.