In the past ten years, there have been tremendous research progresses on massive MIMO systems, most of which stand from the communications viewpoint. A new trend of investigating massive MIMO, especially for the sparse scenario like millimeter wave (mmWave) transmission, is to re-build the transceiver design from array signal processing viewpoint that could deeply exploit the half-wavelength array and provide enhanced performances in many aspects. For example, the high dimensional channel could be decomposed into small amount of physical parameters, e.g., angle of arrival (AoA), angle of departure (AoD), multi-path delay, Doppler shift, etc. As a consequence, transceiver techniques like synchronization, channel estimation, beamforming, precoding, multi-user access, etc., can be re-shaped with these physical parameters, as opposed to those designed directly with channel state information (CSI). Interestingly, parameters like AoA/AoD and multi-path delay are frequency insensitive and thus can be used to guide the down-link transmission from uplink training even for FDD systems. Moreover, some phenomena of massive MIMO that were vaguely revealed previously can be better explained now with array signal processing, e.g., the beam squint effect. In all, the target of this paper is to present an overview of recent progress on merging array signal processing into massive MIMO communications as well as its promising future directions.