Application of the concept of interfacial compliance in analytical thermal stress modeling in electronics and photonics engineering is addressed. The review is based mostly on the author’s research conducted during his tenure with Bell Labs (Basic Research, Area 11, Murray Hill, NJ), University of California (Santa Cruz, CA), Portland State University (Portland, OR), and Small-Business-Innovative-Research (SBIR) ERS Co. The emphasis is on practically important, but often non-obvious and sometime even paradoxical situations.