The cell cycle checkpoint mechanisms ensure the order of cell cycle events to preserve genomic integrity. Among these, the DNA-replication and DNA-damage checkpoints prevent chromosome segregation when DNA replication is inhibited or DNA is damaged. Recent studies have identified an outline of the regulatory networks for both of these controls, which apparently operate in all eukaryotes. In addition, it appears that these checkpoints have two arrest points, one is just before entry into mitosis and the other is prior to chromosome separation. The former point requires the central cell-cycle regulator Cdc2 kinase, whereas the latter involves several key regulators and substrates of the ubiquitin ligase called the anaphase promoting complex. Linkages between these cell-cycle regulators and several key checkpoint proteins are beginning to emerge. Recent findings on post-translational modifications and protein-protein interactions of the checkpoint proteins provide new insights into the checkpoint responses, although the functional significance of these biochemical properties often remains unclear. We have reviewed the molecular mechanisms acting at the DNA-replication and DNA-damage checkpoints in the fission yeast Schizosaccharomyces pombe, and the modifications of these controls during the meiotic cell cycle. We have made comparisons with the controls in fission yeast and other organisms, mainly the distantly related budding yeast.