This paper addresses the problem of dynamic positioning and way-point tracking of underactuated autonomous underwater vehicles (AUVs) in the presence of constant unknown ocean currents and parametric modelling uncertainty. A non-linear adaptive controller is proposed that steers an AUV along a sequence of way-points consisting of desired positions (x, y) in a inertial reference frame, followed by vehicle positioning at the final target point. The controller is first derived at the kinematic level assuming that the ocean current disturbance is known. An exponential observer for the current is then designed and convergence of the resulting closed-loop system trajectories is analysed. Finally, integrator backstepping and Lyapunov based techniques are used to extend the kinematic controller to the dynamic case and to deal with model parameter uncertainty. Simulation results with a dynamic model of an underactuated autonomous underwater shuttle for the transport of benthic labs are presented and discussed.