Cell cycle mutants in the budding and fission yeasts have played critical roles in working out how the eukaryotic cell cycle operates and is controlled. The starting point was Lee Hartwell's 1970s landmark papers describing the first cell division cycle (CDC) mutants in budding yeast. These mutants were blocked at different cell cycle stages and so were unable to complete the cell cycle, thus defining genes necessary for successful cell division. Inspired by Hartwell's work, I isolated CDC mutants in the very distantly related fission yeast. This started a program of searches for mutants in fission yeast that revealed a range of phenotypes informative about eukaryotic cell cycle control. These included mutants defining genes that were rate-limiting for the onset of mitosis and of the S-phase, that were responsible for there being only one S-phase in each cell cycle, and that ensured that mitosis only took place when S-phase was properly completed. This is a brief account of the discovery of these mutants and how they led to the identification of cyclin-dependent kinases as core to these cell cycle controls.