The accuracy of channel state information (CSI) acquisition directly affects the performance of millimeter wave (mmWave) communications. In this article, we provide an overview on CSI acquisition, including beam training and channel estimation for mmWave massive multiple-input multiple-output systems. The beam training can avoid the estimation of a high-dimension channel matrix while the channel estimation can flexibly exploit advanced signal processing techniques. In addition to introducing the traditional and machine learning-based approaches in this article, we also compare different approaches in terms of spectral efficiency, computational complexity, and overhead.