This review article provides an overview and assessment of the bayonet tube heat exchanger in its concentric tube configuration. The article begins with a brief historical sketch of its use in three main contexts: in the process industries, especially in waste heat recovery; in geotechnical engineering, in permafrost stabilization; and in medicine, especially in cryosurgery. A conceptual outline describing the main heat transfer features of the device in counterflow, parallel flow, and cross flow situations follows. Particular attention is paid to the implications of thermal coupling between the inner tube flow, the annular (return) flow and the external fluid flow. The main text is divided into two parts: Experimental studies and Theoretical studies. Each of these is subdivided into two complementary sections: hydraulic studies, in which the emphasis is placed on fluid flow characteristics, especially in the U-bend at the end of the tube; and thermal studies, emphasizing the convective heat transfer characteristics. Each subsection is further divided to permit separate discussion of laminar, transitional and turbulent flow under steady, single-phase conditions. Experimental data are systematically compared with numerical predictions to provide a comprehensive survey of the effect of the independent variables (flow rate, tube geometry, and fluid properties) on the dependent variables (pressure drop, heat transfer rate). Experimental and numerical data are combined to develop empirical correlations for pressure drop and heat transfer. The final section examines the above findings to uncover the limitations of our current knowledge and thereby suggest profitable avenues for future research. There are 47 references listed at the end of the article.