The rapid transition towards an inverter-dominated power system has reduced the inertial response capability of modern power systems. As a solution, inverters are equipped with control strategies, which can emulate inertia by exchanging power with the grid based on frequency changes. This paper discusses the various current control techniques for application in these systems, known as virtual inertia systems. Some classic control techniques like the proportional-integral, the proportional-resonant, and the hysteresis control are presented first, followed by the design and discussion of two more advanced control techniques based on model prediction and machine learning, respectively. MATLAB/Simulink-based simulations are performed, and results are presented to compare these control techniques in terms of harmonic performance, switching frequency, and transient response.