Mobility may degrade the performance of nextgeneration vehicular networks operating at the millimeter-wave spectrum: frequent mis-alignment and blockages require repeated beam-training and handover, with enormous overhead. Nevertheless, mobility induces temporal correlations in the communication beams and in blockage events. In this paper, an adaptive design is proposed, that learns and exploits these temporal correlations to reduce the beam-training overhead and make handover decisions. At each time-slot, the serving base station (BS) decides to perform either beam-training, data communication, or handover, under uncertainty in the system state. The decision problem is cast as a partially observable Markov decision process, with the goal to maximize the throughput delivered to the user, under an average power constraint. To address the high-dimensional optimization, an approximate constrained point-based value iteration (C-PBVI) method is developed, which simultaneously optimizes the primal and dual functions to meet the power constraint. Numerical results demonstrate a good match between the analysis and a simulation based on 2D mobility and 3D analog beamforming via uniform planar arrays at both BSs and UE, and reveal that C-PBVI performs near-optimally, and outperforms a baseline scheme with periodic beam-training by 38% in spectral efficiency. Motivated by the structure of C-PBVI, two heuristics are proposed, that trade complexity with sub-optimality, and achieve only 4% and 15% loss in spectral efficiency. Finally, the effect of mobility and multiple users on blockage dynamics is evaluated numerically, demonstrating superior performance over the baseline scheme. Index Terms-Blockage, beam training, handover, millimeter wave, Markov decision process, point based value iteration. I. INTRODUCTION C URRENT sub-6 GHz vehicular communication systems cannot support the demand of future applications such as autonomous driving, augmented reality and infotainment, due to limited bandwidth availability [2]. To this end, new Manuscript