To learn to read, the brain must repurpose neural systems for oral language and visual processing to mediate written language. We begin with a description of computational models for how alphabetic written language is processed. Next, we explain the roles of a dorsal sublexical system in the brain that relates print and speech, a ventral lexical system that develops the visual expertise for rapid orthographic processing at the word level, and the role of cognitive control networks that regulate attentional processes as children read. We then use studies of children, adult illiterates learning to read, and studies of poor readers involved in intervention, to demonstrate the plasticity of these neural networks in development and in relation to instruction. We provide a brief overview of the rapid increase in the field's understanding and technology for assessing genetic influence on reading. Family studies of twins have shown that reading skills are heritable, and molecular genetic studies have identified numerous regions of the genome that may harbor candidate genes for the heritability of reading. In selected families, reading impairment has been associated with major genetic effects, despite individual gene contributions across the broader population that appear to be small. Neural and genetic studies do not prescribe how children should be taught to read, but these studies have underscored the critical role of early intervention and ongoing support. These studies also have highlighted how structured instruction that facilitates access to the sublexical components of words is a critical part of training the brain to read.