This Review offers quantitative and qualitative analyses of various compact and micro heat exchangers (C-MHXs) in terms of the friction factor, Nusselt number, and heat transfer augmentation mechanism. The C-MHXs, which have already been implemented in industry, are analyzed along with brand-new heat transfer technologies. Pressure drop and Nusselt number are used to characterize the performance of the heat transfer technologies and specifically to ascertain their appropriateness in analyzing C-MHXs. A precise analysis of the correlations reveals that the design parameters must be carefully examined before selecting a suitable correlation. In addition to the quantitative and qualitative analyses, computational fluid dynamics analysis used to design the C-MHXs is also compared with experimental analysis found in the literature. This review of C-MHX technologies will hopefully encourage and motivate more in-depth research into energy-efficient heat transfer devices.