There are many various chromosomal and gene mutations in human cancer cells. The total mutation rate in normal human cells is 2·10(-7) mutations/gene/division. From 6 to 12 carcinogenic mutations can arise by the end of the life, and these can affect the structure of ~150 protooncogenes and genes encoding suppressors of tumor growth. However, this does not explain the tens and hundreds of thousands of mutations detectable in cancer cells. Mutation is any change of nucleotide sequence in cellular DNA. Gene mutations are mainly consequences of errors of DNA polymerases, especially of their specialized fraction (inaccurate DNA polymerases β, ζ, η, θ, ι, κ, λ, µ, σ, ν, Rev1, and terminal deoxynucleotidyl transferase, and only polymerases θ and σ manifest a slight 3'-exonuclease activity) and also consequences of a decrease in the rate of repair of these errors. Inaccurate specialized human polymerases are able to synthesize DNA opposite lesions in the DNA template, but their accuracy is especially low during synthesis on undamaged DNA. In the present review fundamental features of such polymerases are considered. DNA synthesis stops in the area of its lesion, but this block is overcome due to activities of inaccurate specialized DNA polymerases. After the lesion is bypassed, DNA synthesis is switched to accurate polymerases α, δ, ε, or γ. Mechanisms of direct and reverse switches of DNA polymerases as well as their modifications during carcinogenesis are discussed.