The structure and inherent quality of contemporary power systems have undergone significant changes due to the exponential increase in the penetration of renewable resources. Today's power systems face new technical barriers due to the utilization of power electronics-based distributed generation resources and the challenges in ensuring their secure operation. In addition to increased unpredictability and variability, the rising share of renewable resources in power generation has also led to a reduction in the rotational inertia of power systems. Nowadays, extreme weather events impose staggering economic and social costs on human societies. Despite the low probability of occurrence of such events, their considerable intensity and impact on the secure operation of power systems have drawn widespread attention toward enhancing network resilience. Mobile energy storage systems can improve grid resilience and security against events such as power outages, load fluctuations, equipment failures, and other unforeseen incidents in the power network. With their mobility capability, these systems can be rapidly deployed at required locations to help supply electricity during critical times. This paper discusses various measures to enhance power system resilience and outlines potential challenges for future research.