Phased array radars have remarkable advantages over radars with single-element antenna in terms of agility, flexibility, robustness, and reconfigurability. Current pure-electronic phased array radars face challenges when operating with a large frequency tunable range and/or with broad instantaneous bandwidth. Microwave photonics, which allows wide bandwidth, flat frequency response, low transmission loss, and immunity to electromagnetic interference, is a promising solution to cope with issues faced by pure electronics. In this paper, we introduce a general architecture of microwave photonic array radar systems and review the recent advancement of optical beamforming networks. The key elements for modelling the response of the true time delay (TTD) and/or phase-shifting unit are presented and discussed. Two typical array antenna structures are introduced, i.e., microwave photonic phase shifter based array and optical true time delay based array, of which the principle and typical implementations are described. High-resolution inverse synthetic aperture radar (ISAR) imaging is also realized based on a microwave photonic array radar. The possibility of on-chip integration of the microwave photonic array radar is discussed.