A number of error-prone DNA polymerases is found among eukaryotes from yeasts up to mammalia including humans. According to the partial homology of a primary structure, they are united in families B, X, Y and display high infidelity on uninjured DNA-template, whereas they are rather accurate on DNA injuries. These DNA polymerases are characterized by the probability of base substitutions or frame shifts of 10(-3) to 7.5 x 10(-1) on DNA injuries, whereas the probability of spontaneous mutagenesis per replicated nucleotide accounts 10(-10) - 10(-12). Inaccurate DNA polymerases are terminal deoxynucleotidyl transferase (TdT), DNA polymerases beta, zeta, kappa, eta, iota, lamda, mu, and Rev1. Their principal properties are described in this review. All of the polymerases under study are deprived of the corrective 3'-->5' exonucleolytic activity. The specialization of these polymerases is contained in the capability to synthesize opposite DNA lesions (not eliminated by multiple repair systems) that is explained by the flexibility of their active sites or by the limited capability to exhibit the TdT activity. Classic DNA polymerases alpha, delta, epsilon, and gamma cannot elongate the primers with mismatched nucleotides on their 3'-ends (that leads to the replication block), whereas some of the specialized polymerases can do it. It is accompanied by the overcoming of a replication block, often with the expense of an elevated mutagenesis. How can a cell live under the conditions of such a huge infidelity of many DNA polymerases? Error-prone DNA polymerases are not found in all tissues though some of them are essential for an organism survival. Furthermore, cells must not allow for these polymerases to work effectively on uninjured DNA. After bypass of a lesion on DNA-template, it is necessary, as soon as possible, to switch catalysis of the DNA synthesis from the specialized polymerases on the relatively accurate DNA polymerases delta and epsilon (fidelity of 10(-5) - 10(-6)). It is made by the formation of the complexes of polymerases delta or epsilon with PCNA and replicative factors RP-A and RF-C. Such highly processive complexes manifest the bigger affinity to the correct primers than the specialized DNA polymerases do. The switching is stimulated by distributivity or weak processivity of the specialized DNA polymerases. The accuracy of these polymerases are augmented by the action of the corrective 3'-exonucleolytic function of DNA polymerases delta and epsilon as well as by the autonomous 3'-->5' exonucleases which are widespread among the representatives of the whole phylogenetic tree. Exonucleolytic correction slows down the replication in the presence of lesions in DNA-template but makes the replication more accurate that decreases the probability of mutagenesis and carcinogenesis.