Similar and dissimilar material joints of AISI grade 304 (1.4301) and AISI grade 316 (1.4401) austenitic stainless steel by solid state diffusion bonding and transient liquid phase (TLP) bonding are of interest to academia and industry alike. Appropriate bonding parameters (bonding temperature, bonding time, and bonding pressure) as well as suitable surface treatments, bonding atmosphere (usually high vacuum or protective gas) and interlayers are paramount for successful bonding. The three main parameters (temperature, time, and pressure) are interconnected in a strong non-linear way making experimental data important. This work reviews the three main parameters used for solid state diffusion bonding, TLP bonding and to a smaller degree hot isostatic pressing (HIP) of AISI grade 304 and AISI grade 316 austenitic stainless steel to the aforementioned materials (similar joints) as well as other materials, namely commercially pure titanium, Ti-6A-4V, copper, zircaloy and other non-ferrous metals and ceramic materials (dissimilar joints).