This work is a review of our recent analytical advances of the evolution of surface water solitary waves in Miles and Jeffreys' theories of wind wave interaction in water of finite depth. Although many works have been conducted based on Miles and Jeffreys' approach, only a few studies have been carried out on finite depth. The present review is divided into two major parts. The first corresponds to the surface water waves in a linear regime and its nonlinear extensions. In this part, Miles' theory of wave amplification by wind is extended to the case of finite depth. The dispersion relation provides a wave growth rate depending on depth. A dimensionless water depth parameter, depending on the depth and a characteristic wind speed, induces a