<p>This review aims to present a comprehensive historical account of both experimental and numerical investigations into the flow of non-Newtonian fluids around a sphere. Non-Newtonian fluids comprise a broad spectrum of soft materials, each characterized by distinct rheological responses under shear and extensional deformation. Although the geometry of a sphere may appear deceptively simple, the flow that develops around it involves coupled shear and extensional components, thereby eliciting a wide range of rheological phenomena, including shear-thinning, viscoelastic, and thixotropic effects that are absent in Newtonian systems. Sustained scientific interest in this classical problem has led to extensive research over the past several decades, employing both laboratory experiments and numerical simulations to unravel the fundamental mechanisms governing such flows. In this review, we systematically categorize non-Newtonian fluids by their rheological characteristics and trace the historical progression of studies on sphere–fluid interactions within each class. Particular emphasis is placed on highlighting seminal contributions that have shaped the current understanding, as well as recent advances that leverage modern computational techniques. We further identify emerging directions that highlight unresolved challenges and outline promising avenues for future research in non-Newtonian flow around spheres.</p> Graphical abstract <p></p>