This chapter presents the unmanned underwater vehicle (UUV) equations of motion using the results of Fossen. The nonlinear model presented in this chapter is mainly intended for control systems design in combination with system identification and parameter estimation. The resulting model is decoupled into longitudinal and lateral motions such that autopilots for speed, depth/diving and heading control can be designed. The motivation for using nonlinear theory is that one model can cover the whole flight envelope of the UUV, instead of linearising the model about many working points and using gain scheduling between these. In addition, physical model properties in terms of first principles are not destroyed which is a primary problem associated with linearising a plant. Finally, nonlinear optimisation methods are used as a tool for system identification, while proportional-integral-denvative (PID) control and backstepping demonstrate how nonlinear autopilots can be designed.