Gaining facility with spelling is an important part of becoming a good writer. Here we review recent work on how children learn to spell in alphabetic writing systems. Statistical learning plays an important role in this process. Young children learn about some of the salient graphic characteristics of written texts and attempt to reproduce these characteristics in their own productions even before they use letters to represent phonemes. Later, children apply their statistical learning skills to links between phonemes and spellings, including those that are conditioned by context and morphology. Children use what they know about language and about letter names when learning about spelling, and learning to spell in turn influences their ideas about language. Although children learn about some aspects of spelling implicitly, explicit instruction has an important role to play. We discuss some implications of the research for the design of that instruction.