Organic-inorganic hybrid perovskites exhibit superior optoelectrical properties and have been widely used in photodetectors. Perovskite photodetectors with excellent detectivity have great potential for developing artificial photonic synapses which can merge data transmission and storage. They are highly desired for next generation neuromorphic computing. The recent progress of perovskite photodetectors and their application in artificial photonic synapses are summarized in this review. Firstly, the key performance parameters of photodetectors are briefly introduced. Secondly, the recent research progress of photodetectors including photoconductors, photodiodes, and phototransistors is summarized. Finally, the applications of perovskite photodetectors in artificial photonic synapses in recent years are highlighted. All these demonstrate the great potential of perovskite photonic synapses for the development of artificial intelligence.