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This paper reviews the recent advances in the field of radio frequency signal processing using photonic devices and subsystems or microwave photonic (MWP) signal processing. We focus our attention on the results reported during the last six years, as previous work has been adequately addressed in previous review papers. After a brief introduction to the basic concepts involved in MWP signal processing, we focus our attention on the most significant advances reported by different research groups in overcoming their main limitation factors. Recent advances in the emergent topic of integrated MWP signal processors are also covered and the novel approaches toward the evaluation of the main figures of merit are discussed. New proposed applications and future directions of work are also considered.