What is inflection? Is it part of language morphology, syntax or both? What are the basic units of inflection and how do speakers acquire and process them? How do they vary across languages? Are some inflection systems somewhat more complex than others, and does inflectional complexity affect the way speakers process words? This chapter addresses these and other related issues from an interdisciplinary perspective. Our main goal is to map out the place of inflection in our current understanding of the grammar architecture. In doing that, we will embark on an interdisciplinary tour, which will touch upon theoretical, psychological, typological, historical and computational issues in morphology, with a view to looking for points of methodological and substantial convergence from a rather heterogeneous array of scientific approaches and theoretical perspectives. The main upshot is that we can learn more from this than just an additive medley of domain-specific results. In the end, a cross-domain survey can help us look at traditional issues in a surprisingly novel light.