Millimeter wave (mmWave) and massive multiple-input multiple-output (MIMO) are two enabling technologies in fifth-generation (5G) mobile cellular systems. As mmWave makes use of large available bandwidths, the corresponding sampling rates of the digital-to-analog converters (DACs) and analog-to-digital converters (ADCs) scale up, resulting in high power consumption and hardware implementation complexity. The use of large number of antennas also considerably increases the hardware cost if each radio frequency (RF) chain has its dedicated DACs/ADCs. To reduce implementation costs, it is desirable to reduce the DACs/ADCs resolution in mmWave and massive MIMO systems. Employing few- and especially 1-bit DACs/ADCs radically changes both the theory and practice of communication. To enable low-resolution quantization in practical systems, we are working on several critical transceiver design aspects such as pulse shaping, filtering, precoding and time-frequency synchronization optimization.