The morphological structure of complex words impacts how they are processed during visual word recognition. This impact varies over the course of reading acquisition and for different languages and writing systems. Many theories of morphological processing rely on a decomposition mechanism, in which words are decomposed into explicit representations of their constituent morphemes. In distributed accounts, in contrast, morphological sensitivity arises from the tuning of finer-grained representations to useful statistical regularities in the form-to-meaning mapping, without the need for explicit morpheme representations. In this theoretically guided review, we summarize research into the mechanisms of morphological processing, and discuss findings within the context of decomposition and distributed accounts. Although many findings fit within a decomposition model of morphological processing, we suggest that the full range of results is more naturally explained by a distributed approach, and discuss additional benefits of adopting this perspective.