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This paper aims to provide a comprehensive review of the literature and to impart a perspective on the current status and future directions for fundamentals of flow around and heat transfer from a square cylinder with modified corners. The focus is on how rounded, chamfered, recessed, and cut corners of a square cylinder impact the wake structure, flow instability, fluid forces, vortex dynamics, wake width, vortex formation length, boundary layer thickness, displacement thickness, transition to turbulence, drag crisis, and heat transfer. A circular cylinder undergoes drag crisis flow while a square cylinder does not. Sufficiently rounded corners can rejuvenate the drag crisis flow. The corner modifications encompassing heat transfer performance from low to high can be sorted out as sharp, cut, rounded, and chamfered, given the same scale of modifications. Based on the review and analysis of data in the literature, the optimal corner modifications are suggested for reduced forces and enhanced heat transfer. The research gap in the literature is identified and put forward for future investigations. [Display omitted] • Flow around and heat transfer from a square cylinder with modified corners are reviewed. • Focus is on how rounded, chamfered, recessed, and cut corners impact the wake structure. • Flow instability, fluid forces, transition, drag crisis, and heat transfer are summarized. • No drag crisis flow for square cylinder, but sufficiently rounded corners can rejuvenate it. • Optimal corner modifications are suggested for reduced forces and enhanced heat transfer. [ABSTRACT FROM AUTHOR]