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The Keynote Paper reviews and highlights over 40 years of research on solutions for steady-state and transient thermal constriction and spreading resistances, and thermomechanical models for contact, gap and joint resistances of joints formed by conforming rough surfaces, nonconforming smooth surfaces, and nonconforming rough surfaces. Microgap and macrogap thermal resistance and conductance models are reviewed, and important relations and correlation equations are presented. Contact microhardness, determined by Vickers indenters, are correlated and incorporated into the contact model for conforming rough surfaces. Microhardness parameters are correlated with Brinell hardness values. Elastoplastic contact models for joints formed by smooth sphere-smooth flat and conforming rough surfaces are presented. A simple thermomechanical model for microgaps occupied by oil, grease, grease filled with solid particles, and phase change materials such as paraffins is reviewed, and good agreement with recently published data is noted.