In this review paper, we provide perspectives on the implementation of high-performance, wideband, chip-based Brillouin microwave photonic processing subsystems for use in phased array antennas that require processing at every antenna element. We review recent advances in chip-scale Brillouin microwave photonic signal processing systems, including reconfigurable filters, frequency converters, tunable phase shifters, true time delays and microwave sources, which are key functionalities for phased array antennas. We discuss a roadmap for developments of Brillouin-based microwave photonic processors to reach the required performance and compact footprint for implementation in future dynamically reconfigurable phased array antenna systems.