Power quality problem is a hot area in power systems and drives that has drawn the attention of many researchers. This is because of the threat it poses on the health of electrical systems and the cost incurred on utility bills. The problem arises as a result of the need for reactive power to be supplied alongside active power in power transmission and distribution. Unfortunately, reactive power is consumed by almost all components of the system, leading to a shortage. To solve this problem, there is a need to compensate for the lost reactive power. Several researchers have proposed various approaches to mitigate this problem such as thyristor switched capacitor bank, series compensator, series reactor, series var compensator (SVC), Static Synchronous Compensator (STATCOM), synchronous condenser and others. In order to further draw attention in this area, this work investigates a number of research papers on power compensation techniques and draw up challenges from each work that can be considered for further investigation. To this end, each research paper reviewed is evaluated in terms of problem solved, technique used, and results obtained. It therefore offers ample opportunities for researchers to explore in improving power quality and power system safety.