Triple concentric-tube heat exchangers are used widely in refrigeration, drying, energy storage, chemical systems, and the food industry. To handle excessive temperature differences, the heat transfer area, as an option, the heat exchanger’s length, is necessary to be increased. Triple tubes have a significant advantage in this regard in comparison to double ones. The target of this review is to discuss the most recent publications, including the single-phase flows in these heat exchangers, focusing on the heat transfer and hydrodynamic characteristics, and to classify them with various contemporary aspects. The operating conditions, enhanced surfaces, and sizes, as well as the geometrical parameters, are categorized as being part of experimental, numerical, and analytical research. The studies indicate that the heat transfer characteristics of triple concentric-tube heat exchangers are better than those of double tube heat exchangers. In single-phase studies, the convective and overall heat transfer coefficients, Nusselt number, heat transfer rate, and effectiveness are greater in triple heat exchangers than in double heat exchangers, and the heat exchanger length required to achieve the same heat transfer performance is shorter in triple heat exchangers than in double heat exchangers. Heat transfer surface area increases by adding a concentric third tube. Advanced surfaces enhance heat transfer compared to smooth surfaces and flow turbulence in comparison to smooth surfaces. Heat transfer from triple-one enhanced surfaces is not well-analyzed. Design and use of triple ones as a double one’s alternative should advance shortly.