Millimetre wave (mmWave) is a promising technology to meet the ever-growing data traffic in the future. A major challenge of mmWave communications is the high path loss. In order to overcome this issue, mmWave systems often adopt beamforming techniques, which require robust channel estimation and beam tracking algorithms to maintain an adequate quality of service. This paper proposes a framework of channel estimation and beam tracking for mmWave communications. The proposed framework is designed for vehicular to infrastructure communication but can be extended to other applications as well. First, we propose a multi-stage adaptive channel estimation algorithm called robust adaptive multi-feedback (RAF). The algorithm is based on using the estimated channel coefficient to predict a lower bound for the required number of measurements. Our simulations demonstrate that compared with the existing algorithms, RAF can achieve the desired probability of estimation error (PEE), while on average reducing the feedback overhead by 75.5% and the total channel estimation time by 14%. Second, after estimating the channel in the first step, the paper follows by investigating the extended Kalman filter (EKF) for beam tracking in vehicular communications. A crucial part of EKF is the calculation of Jacobian matrices. We show that the model used in the previous work, which was based on the angles of arrival and departure, is not suitable for vehicular communications. This is due to the complexity in the calculation of Jacobian matrices. A new model is proposed for EKF in mmWave vehicular communications which is based on position, velocity and channel coefficient. Closed-form expressions are derived for the Jacobians used in EKF which facilitate the implementation of the EKF tracking algorithm in the proposed model. Finally, we provide an extensive number of simulations to substantiate the robustness of the framework as well as presenting the analytical results on the PEE of the RAF algorithm.Index Terms-Millimeter wave, multiple-input multiple-output (MIMO), channel estimation, beamforming, analog beamforming, beam tracking, Extended Kalman filter (EKF).