The functioning of the eukaryotic genome depends on efficient and accurate DNA replication and repair. The process of replication is complicated by the ongoing decomposition of DNA and damage of the genome by endogenous and exogenous factors. DNA damage can alter base coding potential resulting in mutations, or block DNA replication, which can lead to double-strand breaks (DSB) and to subsequent chromosome loss. Replication is coordinated with DNA repair systems that operate in cells to remove or tolerate DNA lesions. DNA polymerases can serve as sensors in the cell cycle checkpoint pathways that delay cell division until damaged DNA is repaired and replication is completed. Eukaryotic DNA template-dependent DNA polymerases have different properties adapted to perform an amazingly wide spectrum of DNA transactions. In this review, we discuss the structure, the mechanism, and the evolutionary relationships of DNA polymerases and their possible functions in the replication of intact and damaged chromosomes, DNA damage repair, and recombination.