Negative regulator of DNA damage repair which specifically deubiquitinates monoubiquitinated FANCD2. Also involved in PCNA-mediated translesion synthesis (TLS) by deubiquitinating monoubiquitinated PCNA. Has almost no deubiquitinating activity by itself and requires the interaction with WDR48 to have a high activity. Thiol-dependent hydrolysis of ester, thioester, amide, peptide and isopeptide bonds formed by the C-terminal Gly of ubiquitin (a 76-residue protein attached to proteins as an intracellular targeting signal). Interacts with FANCD2 and PCNA. Interacts with WDR48. Interacts with ATAD5; the interaction regulates USP1-mediated PCNA deubiquitination. Autocatalytic cleavage of USP1 following UV irradiation inactivates it leading to an increase in ubiquitinated PCNA, recruitment of POLH and translesion synthesis. Ubiquitinated by the CRL2(KLHDC2) complex following autocatalytic cleavage, leading to its degradation: the CRL2(KLHDC2) complex recognizes the diglycine (Gly-Gly) at the C-terminus. Belongs to the peptidase C19 family.