Heat exchangers using in-tube condensation have great significance in the refrigeration, automotive and process industries. Effective heat exchangers have been rapidly developed due to the demand for more compact systems, higher energy efficiency, lower material costs and other economic incentives. Enhanced surfaces, displaced enhancement devices, swirl-flow devices and surface tension devices improve the heat transfer coefficients in these heat exchangers. This study is a critical review on the determination of the condensation heat transfer coefficient of pure refrigerants flowing in vertical and horizontal tubes. The authors’ previous publications on this issue, including the experimental, theoretical and numerical analyses are summarized here. The lengths of the vertical and horizontal test sections varied between 0.5 m and 4 m countercurrent flow double-tube heat exchangers with refrigerant flowing in the inner tube and cooling water flowing in the annulus. The measured data are compared to theoretical and numerical predictions based on the solution of the artificial intelligence methods and CFD analyses for the condensation process in the smooth and enhanced tubes. The theoretical solutions are related to the design of double tube heat exchangers in refrigeration, air conditioning and heat pump applications. Detailed information on the in-tube condensation studies of heat transfer coefficient in the literature is given. A genetic algorithm (GA), various artificial neural network models (ANN) such as multilayer perceptron (MLP), radial basis networks (RBFN), generalized regression neural network (GRNN), and adaptive neuro-fuzzy inference system (ANFIS), and various optimization techniques such as unconstrained nonlinear minimization algorithm-Nelder-Mead method (NM), non-linear least squares error method (NLS), and Ansys CFD program are used in the numerical solutions. It is shown that the convective heat transfer coefficient of laminar and turbulent condensing film flows can be predicted by means of theoretical and numerical analyses reasonably well if there is a sufficient amount of reliable experimental data. Regression analysis gave convincing correlations, and the most suitable coefficients of the proposed correlations are depicted as compatible with the large number of experimental data by means of the computational numerical methods.