DNA polymerase specifically involved in the DNA repair by translesion synthesis (TLS) (PubMed:10871396). Due to low processivity on both damaged and normal DNA, cooperates with the heterotetrameric (REV3L, REV7, POLD2 and POLD3) POLZ complex for complete bypass of DNA lesions. Inserts one or 2 nucleotide(s) opposite the lesion, the primer is further extended by the tetrameric POLZ complex. In the case of 1,2-intrastrand d(GpG)-cisplatin cross-link, inserts dCTP opposite the 3' guanine (By similarity). Particularly important for the repair of UV-induced pyrimidine dimers (PubMed:10871396). Although inserts the correct base, may cause base transitions and transversions depending upon the context. May play a role in hypermutation at immunoglobulin genes. Forms a Schiff base with 5'-deoxyribose phosphate at abasic sites, but does not have any lyase activity, preventing the release of the 5'-deoxyribose phosphate (5'-dRP) residue. This covalent trapping of the enzyme by the 5'-dRP residue inhibits its DNA synthetic activity during base excision repair, thereby avoiding high incidence of mutagenesis. Targets POLI to replication foci (By similarity). a 2'-deoxyribonucleoside 5'-triphosphate + DNA(n) = diphosphate + DNA(n+1) Binds 2 Mg(2+). Prefers Mg(2+), but can also use Mn(2+). In vitro, can also utilize other divalent cations such as Ca(2+). The enzyme in complex with the DNA substrate binds a third divalent metal cation. The binding of this third divalent cation, which is coordinated by water molecules and two oxygen atoms from DNA and dNTP, is essential for catalyzing the DNA synthesis. Interacts with REV1 (PubMed:14657033). Interacts with monoubiquitinated PCNA, but not unmodified PCNA (By similarity). Interacts with POLI; this interaction targets POLI to the replication machinery (By similarity). Interacts with PALB2 and BRCA2; the interactions are direct and are required to sustain the recruitment of POLH at blocked replication forks and to stimulate POLH-dependent DNA synthesis on D loop substrates (By similarity). Interacts (via C-terminus) with TRAIP. Interacts with ubiquitin (By similarity). Interacts with POLDIP2. Binding to ubiquitinated PCNA mediates colocalization to replication foci during DNA replication and persists at sites of stalled replication forks following UV irradiation. After UV irradiation, recruited to DNA damage sites within 1 hour, to a maximum of about 80%; this recruitment may not be not restricted to cells active in DNA replication. Colocalizes with TRAIP to nuclear foci. Ubiquitous. Up-regulated in proliferating cultured fibroblasts. The catalytic core consists of fingers, palm and thumb subdomains, but the fingers and thumb subdomains are much smaller than in high-fidelity polymerases; residues from five sequence motifs of the Y-family cluster around an active site cleft that can accommodate DNA and nucleotide substrates with relaxed geometric constraints, with consequently higher rates of misincorporation and low processivity. The UBZ3-type zinc finger domain and the PIP-box mediate the interaction with ubiquitinated PCNA and are both necessary for the enzymatic activity in translesion synthesis. Monoubiquitinated by RCHY1/PIRH2. Ubiquitination depends on integrity of the UBZ3-type zinc finger domain and is enhanced by TRAIP. Ubiquitination inhibits the ability of PolH to interact with PCNA and to bypass UV-induced lesions. Belongs to the DNA polymerase type-Y family.