Mobility-on-demand (MOD) services have the potential to significantly improve the adaptiveness and recovery of urban systems, in the wake of disruptive events. But there lacks a comprehensive review on using MOD services for such purposes in addition to serving regular travel demand. This paper presents a review that suggests a noticeable increase within recent years on this topic across four main areas: resilient MOD services, novel usage of MOD services for improving infrastructure and community resilience, empirical impact evaluation, and enabling and augmenting technologies. The review shows that MOD services have been utilized to support anomaly detection, essential supply delivery, evacuation and rescue, on-site medical care, power grid stabilization, transit service substitution during downtime, and infrastructure and equipment repair. Such a versatility suggests a comprehensive assessment framework and modeling methodologies for evaluating system design alternatives that simultaneously serve different purposes. The review also reveals that integrating suitable technologies, business models, and long-term planning efforts offers significant synergistic benefits.