In this paper, the observability properties of automotive powertrains with backlash are analysed. We model the powertrain as a hybrid system in the piecewise affine form and use measurements of the torque and the angular speed of the engine for computing the maximal set of observable states. This set, that is usually non-convex and disconnected, captures in a precise way how the main variables and parameters of the driveline influence the possibility of estimating the shaft twist. Then, we show how to exploit the knowledge of observable states in order to build computationally efficient deadbeat observers for the reconstruction of the powertrain states.