It is the aim of this survey to present a logically coherent overview of recently developed models for the interface between the crystal phase and the mother phase. One of the main uses of the integrated theories to be presented is to calculate the actual bond energies for a particular crystallographic face (hkl) in contact with a particular mother phase. Moreover, the models provide the basis for crystal growth kinetic models which allow the calculation of relative growth rates for different faces. In this way a most reliable prediction of the morphology of the crystal morphology becomes possible. We note that the role of impurities can also be taken into consideration. In this survey paper, a brief survey of the integrated surface roughening and Hartman-Perdok theory is given in section 1. In section 2, basic concepts of regular solution theory are summarized. In section 3, interface models of the solid-fluid interface are developed. These models are apart from regular solution theories based on other  theories of the fluid part of the interface like molecular dynamic studies. In section  4, theories developed in previous sections are applied to certain model systems. In section 5 kinetic models are developed and applied to some crystals growing from the vapor or from solutions.