In the last two decades, single-arm trials (SATs) have been effectively used to study anticancer therapies in well-defined patient populations using durable response rates as an objective and interpretable study endpoints. With a growing trend of regulatory accelerated approval (AA) requiring randomized controlled trials (RCTs), some confusions have arisen about the roles of SATs in AA. This review is intended to elucidate necessary and desirable conditions under which an SAT may be considered appropriate for AA. Specifically, the paper describes (1) two necessary conditions for designing an SAT, (2) eight desirable conditions that help either optimize the study design and doses or interpret the study results, and (3) three additional considerations for construction of estimands, adaptive designs, and timely communication with relevant regulatory agencies. Three examples are presented to demonstrate how SATs can or cannot provide sufficient evidence to support regulatory decision. Conditions and considerations presented in this review may serve as a set of references for sponsors considering SATs to support regulatory approval of anticancer drugs.