Cell division in yeast involves four main processes - cell growth, DNA replication, chromosome separation, and cell division. These occur in distinct phases: interphase consisting of G1, S, and G2 phases, and mitosis. Progression through the cell cycle is regulated by protein kinases like MPF and CDK1 to ensure DNA replication only occurs once per cycle and that the cell grows to the proper size before dividing. Checkpoints in G1, S, G2, and mitosis further ensure replication and division errors are corrected before progression.