Compact heat exchangers are generally of plate-fin, tube-fin and regenerative type. Heat transfer surfaces are made from metals, ceramics, plastics, or special papers. The technological advances in these exchangers are first summarized. Significant advances in the design theory of these exchangers have been made over the past two decades. Some of the areas covered in the paper are: The effectiveness-number of heat transfer units relationship for most practical flow arrangements including the influence of longitudinal wall heat conduction, pressure drop analysis, theoretical and experimental dimensionless heat transfer and pressure drop design data, surface selection and design optimization techniques, computer aided thermal design, fin efficiency, header design and flow mal-distribution, gas-side fouling, and two-phase flows, and exchanger irreversibility evaluation. A state-of-the-art review of these advances has been made in the paper. Finally, the major areas of future research in compact heat exchangers have been identified in order to provide some guidelines to the researchers.