The penetration of renewable energy sources on a large scale in conventional electric networks increases exponentially for environmental preservation. However, the increase in RESs leads to some technical problems that include (a) fluctuations in power production, (b) less or no generation units for power balancing, (c) reduced inertia due to RESs decoupling from the conventional grid using converters. Micro-hydro power plants (MHPPs) are emerging as a mature balancing technology and a great alternative to large hydropower plants as they encounter population displacement and many environmental problems. Modern pump storage MHPPs uses a power converter between the grid and machine to control the consumption of power during pumping mode. This power electronic interface loses the ability of the rotating mass of the machine to contribute to the grid inertia by making it independent of the grid frequency. This problem is solved through the control of power converters in such a way that the inertia effect is synthesized termed as synthetic inertia. MHPPs can also be operated in a standalone mode where they are not connected to the grid. This paper reviews control schemes applied in literature for the frequency, voltage, and inertia control, in both the grid-connected and standalone modes. This study starts with the standalone MHPPs, covering the literature review and control structure for voltage and frequency control of standalone MHPPs. Then it presents a detailed operation, control principle, synthetic inertia concepts, and architecture of grid-connected MHPPs. The mathematical formulation of the grid, permanent magnet synchronous generator, synthetic inertia inclusion, and control structures, including direct torque control, virtual synchronous machine, and model predictive control, is also presented. Finally, the paper presents the concluding remarks with the comparative analysis of various control structures to include synthetic inertia, its suitability, and future scope for MHPPs.