The chapter provides a computer-based, algorithmic view of issues of lexical processing, ranging from the encoding of input data to the structure of output representations, going through the basic operations of word splitting, storage, access, retrieval, and assembly of intermediate representations. By illustrating the contribution of different computational frameworks (such as finite state automata, hierarchical lexica, artificial neural networks, and statistical language models) to our understanding of aspects of lexical organization, the chapter discusses the implications of theoretical models of morphology for computational models of word processing, as well as the implications of computer models for theoretical issues. In this perspective, much of current work in computational morphology does not only provide a challenging test bed for box and arrow models of lexical knowledge, but it also promises to bridge the persisting gap between theoretical frameworks and behaviourally oriented research in lexical modelling.