The modern power system is progressing from a synchronous machine-based system towards an inverter-dominated system, with a large-scale penetration of renewable energy sources (RESs) like wind and photovoltaics. RES units today represent a major share of the generation, and the traditional approach of integrating themas grid following units can lead to frequency instability. Many researchers have pointed towards using inverters with virtual inertia control algorithms so that they appear as synchronous generators to the grid, maintaining and enhancing system stability. Our paper presents a literature review of the current state-of-the-art of virtual inertia implementation techniques, and explores potential research directions and challenges. The major virtual inertia topologies are compared and classified. Through literature review and simulations of some selected topologies it has been shown that similar inertial response can be achieved by relating the parameters of these topologies through time constants and inertia constants, although the exact frequency dynamics may vary slightly. The suitability of a topology depends on system control architecture and desired level of detail in replication of the dynamics of synchronous generators. We present a discussion on the challenges and research directions which points out several research needs, especially for systems level integration of virtual inertia systems.