Heat transfer enhancement, pumping power and weight minimization in enhanced heat exchangers has long been achieved by deploying tubes with internal surface modifications like microgrooves, ribs, fins, knurls, and dimples with and without tube inserts. This article presents a very extensive review of experimental and computational studies on heat transfer enhancement, which covers convectional and unconventional working fluids under different fluid flow conditions. Compound augmentation with tube surface modifications and inserts has yielded enhancements in the overall heat transfer coefficient of over 116% in the fully developed turbulent flow regime. Exotic fluids like nano-coolants deployed in spiral grooved mircofin tubes yielded 196% enhancement in tube side heat transfer rate for concentrations as low as 0.5% by volume, while the thermal efficiency index measuring the overall enhancement in relation to the pumping power was 75%. However, reviews that address the combined effect of unconventional fluids, surface modifications and tube inserts on the overall thermo-hydraulic performance of annular heat exchangers seem to be limited. Further, nano-coolants aren’t frequently used in the process industry. The goal of this study is to document and evaluate the impact of cost-effective and energy-saving passive enhancement techniques such as tube surface modifications, tube inserts, and annular enhancement techniques on annular heat exchangers used in the process industries with Newtonian and non-Newtonian fluids. This review should be useful to engineers, academics and medical professionals working with non-Newtonian fluids and enhanced heat exchangers.