Significant advances have taken place in the theory, analysis, design and optimization, manufacturing, and technology of compact heat exchangers (CHEs) over the last 20-25 years. The objective of this D. Q. Kern Award paper is to summarize and assess ( where appropriate) these advances in CHEs related to the following specific areas of CHEs: (1) advances in two-fluid exchanger effectiveness and NTU results for highly complex flow arrangements, (2) heat transfer and pressure drop analyses, (3) the role of CFD in the design and analysis of header and manifold design, (4) recuperator design procedure, (5) design data for compact heat exchangers, (6) thermodynamic modeling and analysis, (7) brazing of compact heat exchangers, and (8) advancement in CHEs for new applications such as fuel cells and microturbines. Some challenges and opportunities will be summarized to advance the science and technology further.