Mobility-on-demand (MOD) services have the potential to significantly improve the adaptiveness and recovery of urban logistics and transportation infrastructure, in the wake of disruptive events. This paper presents a survey on the usage of MOD services for resilience improvement (MOD-R) and finds a noticeable increase within recent years on this topic across four main areas: resilient MOD services, novel usage of MOD-R services for improving supply chain resilience, empirical impact evaluation, and supporting technologies. MOD-R services have been utilized for 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. The review reveals integrating electrification, automation, and advanced communication technologies offers significant synergistic benefits. The review also suggests the importance of harnessing the collective capabilities of humans and intelligent machines to effectively implement versatile, multi-functional MOD-R services during crises.