Multi-user millimeter wave (mmWave) massive multi-input multi-output (MIMO) is a promising technology for the next generation mobile communication systems. However, there are still unsolved problems before such commercial MIMO networks are rolled out. One main issue is the hardware cost and power consumption which grow significantly as the number of radio frequency (RF) components increases. To tackle this issue, we consider to deploy one-bit analog-to-digital converters (ADCs) and digital-to-analog converters (DACs) at the base station (BS), and study uplink (UL)/downlink (DL) channel estimation and DL precoding techniques for the associated MIMO systems with one-bit ADCs/DACs. Specifically, we first formulate the UL channel estimation as an one-bit compressed sensing problem, and then devise an efficient gridless generalized approximate message passing-based (GL-GAMP) algorithm to handle it. Additionally, we develop an exhaustive search based proximal gradient descent method (PGM) for DL channel estimation. Note that with slight modifications, we show that PGM can also be applied to solve the DL precoding problem. Simulation results showcase that our methods have advantages over the state-of-the-art techniques and are able to offer good trade-offs between accuracy and computational complexity, which ultimately indicates their superiority in the application of mmWave MIMO systems with one-bit ADCs/DACs.