<p>A concise review of the mathematical methods available for resolving fluid flow, heat, and mass transfer problems is presented in this paper. In general, the equations pertinent to the transfer of fluid, heat, and mass are partial differential equations that are solved by numerical or semi-analytical, or analytical methods. This review explores the pros and cons of various approaches to solving fluid flow problems. For a better understanding of the various mathematical methods employed to solve governing equations, past research conducted by various researchers is used as a primary source. The exploration of each method studied is done giving importance to its technicality and accessibility. In this review, the key findings that are gathered from various studies that have been done earlier to solve fluid flow problems are categorized into numerical methods, semi-analytical methods, and analytical methods. The review will be beneficial to the researchers to encompass the different methods for solving fluid flow problems.</p>