The complementary relationship of evaporation was first based on the linear feedbacks of land surface evaporation on the atmospheric evaporative demand. Given that the water availability of the land surface changes with constant available energy， it means that the land surface evaporation and the atmospheric evaporative demand change complementarily with equal amount yet opposite directions. Actual evaporation can be estimated with routinely measured meteorological variables based on the complementary relationship. At present， the complementary relationship is generalized to a constitutive relationship describing the nonlinear interactions between the land surface evaporation and the atmospheric evaporative demand. Three generalized nonlinear complementary relationships were proposed： the sigmoid formulation of Han et al. （2012）， the polynomial formulation of Brutsaert （2015）， and the rescaling approach on the independent variable of the polynomial formulation of Crago and Szilagyi （2016）. The three nonlinear complementary relationships adopt different boundary conditions， and employ different approaches to deal with the influences of the land surface water availability， reflecting different understandings on the interactions between the land surface evaporation and the atmospheric evaporative demand. This review summarizes the historical development of the generalized nonlinear complementary relationships with a specific focus on their controversies， and analyzes the differences of the understandings and research approaches， so as to provide a reference for the development of evaporation research.