In the past few years, the application and research community has expressed a lot of interest in managing energy and power while using distributed generation systems. Electricity generation and its usage coordination are vital aspects of energy efficiency that can help in saving energy, decreasing energy costs, and fulfilling global emission objectives. Owing to the relevance of the topic, here, the researchers have presented a comparative and critical review of recent developments in the fields of energy management systems (EMSs) and power management systems (PMSs). Furthermore, the researchers also reviewed the various EMS and PMS methods that could be used for reviewing microgrid (MG) and nanogrid (NG) systems. The EMS for MG and NG systems helps in addressing important economic objectives like minimisation of operational costs after optimising the fuel costs, emission costs, and battery degradation costs, while also improving the life of the MG devices. Alternatively, the PMS helps in addressing technical objectives like improving the stability, flexibility, reliability, and quality of MG and NG systems. The researchers have also discussed the drawbacks and challenges affecting the widespread application of EMSs and PMSs.