The ongoing development of renewable energy and microgrid technologies has gradually transformed the conventional energy infrastructure and upgraded it into a modernized system with more distributed generation and localized energy storage options. Compared with power grids utilizing synchronous generation, inverter-based networks cannot physically provide large amounts of inertia, which means that more advanced and extensive studies regarding stability considerations are required for such systems. Therefore, appropriate analytical methods are needed for the voltage stability analysis of renewable-dominated power systems, which incorporate a large number of inverters and distributed energy sources. This paper provides a comprehensive literature review of voltage stability analyses of power systems with high levels of renewable energy penetration. A series of generalized evaluation schemes and improvement methods relating to the voltage stability of power systems integrated with various distributed energy resources are discussed. The existing voltage stability analysis methods and corresponding simulation verification models for microgrids are also reviewed in a systematic manner. The traditional and improved voltage stability analysis methods are reviewed according to the microgrid operation mode, the types of distributed generators, and the microgrid configurations. Moreover, the voltage stability indices, which play a crucial role in voltage stability assessments, are critically evaluated in terms of the applicable conditions. The associated modeling and simulation techniques are also presented and discussed. This contribution presents guidelines for voltage stability analysis and instability mitigation methods for modern renewable-rich power systems.