Parametric uncertainties and coupled nonlinear dynamics are inherent in quadrotor configuration and infer adaptive nonlinear approaches to be used for flight control system. Numerous adaptive nonlinear and intelligent control techniques, which have been reported in the literature for designing quadrotor flight controller by various researchers, are investigated in this paper. As a priori, each conventional nonlinear control technique is discussed broadly and then its adaptive/observer based augmentation is conferred along with all possible variants. Among conventional nonlinear control approaches, feedback linearization, backstepping, sliding mode, and model predictive control, are studied. Intelligent control approaches incorporating fuzzy logic and neural networks are also discussed. In addition to adaption based parametric uncertainty handling, various other aspects of each control technique regarding stability, disturbance rejection, response time, asymptotic, exponential and finite time convergence etc., are discussed in sufficient depth. The contribution of this paper is the provision of detailed and in depth discussion on quadrotor nonlinear control approaches to the flight control designers.