This paper documents all the important works in the field of conjugate heat transfer study. Theoretical and applied aspects of conjugate heat transfer analysis are reviewed and summarized to a great extent on the light of available literature in this field. Over the years, conjugate heat transfer analysis has been evolved as the most effective method of heat transfer study. In this approach the mutual effects of thermal conduction in the solid and convection in the fluid are considered in the analysis. Various analytical and computational studies are reported in this field. Comprehension of analytical as well as computational studies of this field will help the researchers and scientists who work in this area to progress in their research. That is the focus of this review. Early analytical studies related to conjugate heat transfer are reviewed and summarised in the first part of this paper. Background of theoretical studies is discussed briefly. More importance is given in summarising the computational studies in this field. Different coupling techniques proposed to date are presented in great detail. Important studies narrating the application of conjugate heat transfer analysis are also discussed under separate headings. Hence the present paper gives complete theoretical background of Conjugate heat transfer along with direction to its application envelope. © 2018, CIMNE, Barcelona, Spain.