The modern power system is progressing from a system based on synchronous generators toward systems with high penetration of renewable energy sources (RESs) such as photovoltaic (PV) and wind power generating units which are connected to the grid through inverters. RES units will represent a significant share of the power generation in near future; therefore, the conventional approach of integrating them into the grid may lead to frequency instability. Many researchers have suggested the use of inverters with virtual inertial control methods to act as synchronous generators in the grid and maintain and increase the frequency stability. This paper presents a comprehensive overview of virtual inertial strategies and current control strategies and makes a comprehensive comparison while describing their characteristics. Then, different types of stability analyses in the presented methods are examined and examples of each are presented. In continuation and in addition to the review studies conducted in this field, methods presented with the aim of improving the virtual inertial control are carefully examined and their characteristics according to the number of resources used, the adaptivity of parameters, the use of optimization methods, the issue of coordination between several resources and the type of communication network are studied. Moreover, a comprehensive review of multiple- virtual synchronous generator (VSG) methods to develop and implement the concept of virtual inertia in weak grids are presented. Finally, a discussion of challenges and research directions is presented, particularly pointing to the integration of multiple virtual inertial units at the system level.