A massive hybrid array consists of multiple analog subarrays, with each subarray having its digital processing chain. It offers the potential advantage of balancing cost and performance for massive arrays and therefore serves as an attractive solution for future millimeter-wave (mm- Wave) cellular communications. On one hand, using beamforming analog subarrays such as phased arrays, the hybrid configuration can effectively collect or distribute signal energy in sparse mm-Wave channels. On the other hand, multiple digital chains in the configuration provide multiplexing capability and more beamforming flexibility to the system. In this article, we discuss several important issues and the state-of-the-art development for mm-Wave hybrid arrays, such as channel modeling, capacity characterization, applications of various smart antenna techniques for single-user and multiuser communications, and practical hardware design. We investigate how the hybrid array architecture and special mm-Wave channel property can be exploited to design suboptimal but practical massive antenna array schemes. We also compare two main types of hybrid arrays, interleaved and localized arrays, and recommend that the localized array is a better option in terms of overall performance and hardware feasibility.