Research on speech categorization and phoneme recognition has relied heavily on tasks in which participants listen to stimuli from a speech continuum and are asked to either classify each stimulus (identification) or discriminate between them (discrimination). Such tasks rest on assumptions about how perception maps onto discrete responses that have not been thoroughly investigated. Here, we identify critical challenges in the link between these tasks and theories of speech categorization. In particular, we show that patterns that have traditionally been linked to categorical perception could arise despite continuous underlying perception and that patterns that run counter to categorical perception could arise despite underlying categorical perception. We describe an alternative measure of speech perception using a visual analog scale that better differentiates between processes at play in speech categorization, and we review some recent findings that show how this task can be used to better inform our theories.