The fundamental importance of lexical categories is uncontroversial within both formal and functional approaches to grammatical analysis. But despite the familiarity of this topic and its foundational nature for grammatical description and analysis, it is paradoxically not among the best-studied or -understood topics from either the functionalist or formalist perspective. Both schools of linguistic theory have inherited their basic assumptions and instincts about lexical categories from the structuralist practice of distributional analysis. We briefly survey approaches to the various lexical categories. We then comment on a few issues of strategic value that arise from these approaches, including the importance of clearly distinguishing roots, stems, words, and syntactic units when it comes to issues of lexical categories; the importance of recognizing when distributional tests are similar across languages in principled ways; and the need for the choice of distributional tests to be informed by theoretical hypotheses.