DNA polymerase that functions in several pathways of DNA repair. Involved in base excision repair (BER) responsible for repair of lesions that give rise to abasic (AP) sites in DNA. Also contributes to DNA double-strand break repair by non-homologous end joining and homologous recombination. Has both template-dependent and template-independent (terminal transferase) DNA polymerase activities. Has also a 5'-deoxyribose-5-phosphate lyase (dRP lyase) activity. a 2'-deoxyribonucleoside 5'-triphosphate + DNA(n) = diphosphate + DNA(n+1) Interacts with PCNA. Interacts with PAXX; promoting POLL recruitment to double-strand breaks (DSBs) and stimulation of the end-filling activity of POLL. Interacts with XRCC4; promoting POLL recruitment to double-strand breaks (DSBs) and stimulation of the end-filling activity of POLL. Interacts with NHEJ1/XLF; promoting POLL recruitment to double-strand breaks (DSBs) and stimulation of the end-filling activity of POLL. Belongs to the DNA polymerase type-X family.