Rapid industrialization and its automation on the globe demands increased generation of electrical energy with more reliability and quality. Renewable energy (RE) sources are considered as a green form of energy and extensively used as an alternative source of energy for conventional energy sources to meet the increased demand for electrical power. However, these sources, when integrated to the utility grid, pose challenges in maintaining the power quality (PQ) and stability of the power system network. This is due to the unpredictable and variable nature of generation by these sources. The distributed flexible AC transmission system (DFACTS) devices such as distributed static compensator (DSTATCOM) and dynamic voltage restorer (DVR) play an active role in mitigating PQ issues associated with RE penetration. The performance of DFACTS devices is mostly dependent on the type of control algorithms employed for switching of these devices. This paper presents a comprehensive review of various conventional and adaptive algorithms used to control DFACTS devices for improvement of power quality in utility grids with RE penetration. This review intends to provide a summary of the design, experimental hardware, performance and feasibility aspects of these algorithms reported in the literature. More than 170 research publications are critically reviewed, classified, and listed for quick reference for the advantage of engineers and academician working in this area.