While we know that the neocortex occupies 85% of our brains and that its circuits allow an enormous flexibility and repertoire of behavior (not to mention unexplained phenomena like consciousness), a century after Cajal we have very little knowledge of the details of the cortical circuits or their mode of function. One simplifying hypothesis that has existed since Cajal is that the neocortex consists of repeated copies of the same fundamental circuit. However, finding that fundamental circuit has proved elusive, although partial drafts of a "canonical circuit" appear in many different guises of structure and function. Here, we review some critical stages in the history of this quest. In doing so, we consider the style of cortical computation in relation to the neuronal machinery that supports it. We conclude that the structure and function of cortex honors two major computational principles: "just-enough" and "just-in-time."