A detailed description of a concentric annular heat pipe (CAHP) operation is presented in low to moderate temperature ranges (50-200 degrees C). The steady-state response of a CAHP to various heat fluxes in the evaporator and condenser sections are discussed. Two-dimensional mathematical modeling of the fluid flow and heat transfer in the annular vapor space and the wicks are described. The fundamental aspects and limitations of the operation of a CAHP are also discussed. Previously used numerical and experimental approaches for the analysis of the CAHPs and some related concepts are reviewed. The Navier-Stokes and similar equations are recommended for the simulation of fluid flow and heat transfer in the annular vapor space and the wicks. A number of important concepts, such as two-phase flow, heat transfer in the heat pipe wicks, the vapor-liquid interface conditions, design considerations, testing, and manufacture of a CAHP are also briefly discussed. The results of this research have shown that the available numerical and experimental data in the literature are sufficiently accurate in many applications. However new mathematical models and experimental works are needed for the better design and manufacture of various types of CAHPs.