Surface roughness was an important indicator in the evaluation of a manufacturing process and a product's quality because it can directly affect the wear resistance, sealing performance, and corrosion resistance of parts. The surface quality was more demanding than ever before with the development of modern science and technology. Traditional two-dimensional surface roughness measurement and characterization can hardly meet the requirements, and therefore, three-dimensional measurement and characterization was becoming a research hotspot because it can comprehensively and truly reflect the surface topography. This study reviewed the development history of areal surface roughness, investigated the state-of-the-art areal surface roughness parameters and standards, systematically analyzed the relationship between surface topography and functional characteristics, and summarized the applications of areal surface roughness parameters in manufacturing, biomedical, tribology, materials science, etc. As the research advances (for example, the further study of traceability and repeatability of areal surface topography measurements, the parameters characterization system, and the maturity of additive manufacturing) and measurement techniques are developed, three-dimensional surface roughness parameters were sure to be completed and popularized in the future. It will better combine with the actual functions to predict the working performance and ensure the surface quality of the workpiece.