The family of poly (ADP-ribose) polymerases (PARPs) consists of 17 members, which have been demonstrated as having effects on a series of cellular processes, including DNA replication and repair. PARP inhibitors (PARPi) suppress DNA repair through “PARP trapping”, thus, constitute an important treatment option for cancer nowadays. In addition, PARP inhibition and homologous recombination repair (HRR) defects are synthetically lethal, giving a promising therapeutic for homologous recombination repair deficient (HRD) tumors including BRCA mutation. However, overlapping hematologic toxicity causes PARPi to fail in combination with some first-line chemotherapies. Furthermore, recent literature has demonstrated that PARP1 inhibition and PARP1-DNA trapping are key for antitumor activity in HRD cancer models. Currently approved PARPi have shown varying levels of selectivity for the entire 17-member PARP family, hence contribute to toxicity. Together, these findings above have provided the necessity and feasibility of developing next-generation PARPi with improved selectivity for PARP1, expanding significant clinical values and wide application prospects both in monotherapy and combination with other anticancer agents. In this review, we summery the latest research of current approved PARPi, discuss the current status and future promise of next-generation PARP1-selective inhibitor AZD5305, including its reported progress up to now and anticipated impact on clinical.