Rotary compressors have been employed in heating and cooling for more than a century and are ubiquitous in daily life but there has not been any comprehensive record of their development and technological advances. This review paper attempts to provide a comprehensive account of the advances in R&D and design evolution of these rotary compressors since their inception, namely the sliding vane compressor, rolling piston compressor, and their design variants in open literature. This is to showcase the current state-of-the-art for these compressors so that researchers can use it as a basis for future work. Based on authors’ insight, inter-disciplinary research combined with advancements in ‘disruptive’ technology such as artificial intelligence and advancements in additive manufacturing might be a promising research direction to bring about improvements in rotary compressor performance to meet mankind’s growing needs for cooling and heating applications.