The increasingly demanding objectives for next generation wireless communications have spurred recent research activities on multi-antenna transceiver hardware architectures and relevant intelligent communication schemes. Among them belong the Full Duplex (FD) Multiple-Input Multiple-Output (MIMO) architectures, which offer the potential for simultaneous uplink and downlink operations in the entire frequency band. However, as the number of antenna elements increases, the interference signal leaking from the transmitter of the FD radio to its receiver becomes more severe. In this article, we present a unified FD massive MIMO architecture comprising analog and digital transmit and receive BeamForming (BF), as well as analog and digital SI cancellation, which can be jointly optimized for various performance objectives and complexity requirements. Performance evaluation results for applications of the proposed architecture to fully digital and hybrid analog and digital BF operations using recent algorithmic designs, as well as simultaneous communication of data and control signals are presented. It is shown that the proposed architecture, for both small and large numbers of antennas, enables improved spectral efficiency FD communications with fewer analog cancellation elements compared to various benchmark schemes. The article is concluded with a list of open challenges and research directions for future FD massive MIMO communication systems and their promising applications.