The live, attenuated oral poliovirus vaccine (OPV) provides a powerful tool for controlling and stopping the transmission of wild polioviruses (WPVs), although the risks of vaccine-associated paralytic polio (VAPP) and circulating vaccine-derived poliovirus (cVDPV) outbreaks exist as long as OPV remains in use. Understanding the dynamics of cVDPV emergence and outbreaks as a function of population immunity and other risk factors may help to improve risk management and the development of strategies to respond to possible outbreaks. We performed a comprehensive review of the literature related to the process of OPV evolution and information available from actual experiences with cVDPV outbreaks. Only a relatively small fraction of poliovirus infections cause symptoms, which makes direct observation of the trajectory of OPV evolution within a population impractical and leads to significant uncertainty. Despite a large global surveillance system, the existing genetic sequence data largely provide information about transmitted virulent polioviruses that caused acute flaccid paralysis, and essentially no data track the changes that occur in OPV sequences as the viruses transmit largely asymptomatically through real populations with suboptimal immunity. We updated estimates of cVDPV risks based on actual experiences and identified the many limitations in the existing data on poliovirus transmission and immunity and OPV virus evolution that complicate modeling. Modelers should explore the space of potential model formulations and inputs consistent with the available evidence and future studies should seek to improve our understanding of the OPV virus evolution process to provide better information for policymakers working to manage cVDPV risks.