High-impact and low-probability (HILP) extreme events can cause severe damage to power systems. Microgrids (MGs) with distributed generation resources provide a viable solution for the resilience enhancement of distribution networks during extreme events. In this paper, resilience-oriented modeling details are appropriately presented across four dimensions: modeling objectives and metrics, resilience scenarios, control methods and resilience-oriented strategies. Three types of objective functions are commonly used in existing literature: load maximization, cost minimization and frequency stabilization. To mimic realistic resilience scenarios, uncertainty information, contingencies, distributed generation resources and interdependencies between power systems and other networks (e.g. gas networks) are main factors that need to be considered. Energy management system, optimal power flow and dynamic control are three basic approaches utilized to model resilient power systems. As far as operational strategies in relation to network topologies are concerned, four types are typically met in the literature, these being existing MGs for network resilience, dynamic formation of MGs, islanding schemes of MGs and networked MGs. Different types of MGs and different control methods are also appropriately presented in this part. Finally, research challenges are identified and several future research directions are provided. • Research on resilience-oriented modeling and operational strategies reviewed. • Objective functions and metrics used for resilience-oriented optimization summarized. • Key points to capture the main features of extreme events summarized and discussed. • Basic approaches to model resilient power systems summarized. • Microgrid-based network topologies and operational strategies explained and discussed. [ABSTRACT FROM AUTHOR]