An overview of recent work on nonlinear Couette flow in a dilute gas is presented. The analysis is made within the framework of the Boltzmann equation by following three different and complementary routes: (i) the application of the Grad method to the Boltzmann equation, (ii) the analytical solutions of the BGK and ellipsoidal statistical (ES) models, and (iii) the use of the Direct Simulation Monte Carlo (DSMC) method to numerically solve the true Boltzmann equation. In the bulk domain, we found a solution characterized by constant pressure, and linear velocity and parabolic temperature profiles with respect to a scaled variable. The main transport coefficients of the problem are obtained as nonlinear functions of the reduced shear rate. The predictions of the kinetic models and those obtained by using the Grad method are compared with both molecular dynamics and Monte Carlo simulations. The comparison shows that the results derived from the kinetic models present a better agreement with the computer simulations than those obtained from the Grad method, especially in the case of the ES model.