Static mixers are widely used in various industrial applications to intensify the laminar mixing of non-Newtonian fluids. Non-Newtonian fluids can be categorized into (1) time-independent, (2) time-dependent, and (3) viscoelastic fluids. Computational fluid dynamics studies on the laminar mixing of viscoelastic fluids are very limited due to the complexity in incorporating the multiple relaxation times and the associated stress tensor into the constitutive equations. This review paper provides recommendations for future research studies while summarizing the key research contributions in the field of non-Newtonian fluid mixing using static mixers. This review discusses the different experimental techniques employed such as electrical resistance tomography, magnetic resonance imaging, planar laser-induced fluorescence, and positron emission particle tracking. A comprehensive overview of the mixing fundamentals, fluid chaos, numerical characterization of fluid stretching, development of pressure drop correlations, and derivations of generalized Reynolds number is also provided in this review paper.