Millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) has been considered as a key enabler for the fifth-generation (5G) communications. It is essential to design and test mmWave 5G devices under various realistic scenarios since the radio propagation channels pose intrinsic limitations on the performance. This requires emulating realistic dynamic mmWave channels in a reproducible manner in laboratories, which is the goal of this article. In this contribution, we first illustrate the dominant-cluster(s) concept, where the nondominant clusters in the mmWave channels are pruned, for mmWave 5G devices applying massive MIMO beamforming. This demonstrates the importance and necessity to accurately emulate the mmWave channels at a cluster level rather than the composite-channel level. Thus, an over-the-air (OTA) emulation strategy for dynamic mmWave channels is proposed based on the concept of the dominant cluster(s) in a sectored multiprobe anechoic chamber (SMPAC). The key design parameters, including the probe number and the angular spacing of probes, are investigated through comprehensive simulations. A cost-effective switch circuit is also designed for this purpose and validated in the simulation. Furthermore, a dynamic mmWave channel measured in an indoor scenario at 28-30 GHz is presented, where the proposed emulation strategy is also validated by reproducing the measured reality.