An integrated photonic diffractive deep neural network ( ID^2 NN) is one of the most exciting cross-discipline fields of artificial intelligence and optical computing, combining deep learning with the power of light-speed processing on an integrated platform. We know that neural network in a digital computer is based on transistors, which have significant challenges in keeping pace with Moore's law and limited real-time processing applications due to the increased computational costs associated with them. However, with remarkable progress and advancement in silicon photonic integrated circuits over the last few decades, ID^2 NNย hold the promise of on-chip miniaturisation and high-speed performance with low power consumption. This paper covers the essential theoretical background for constructing theย ID^2 NNย and reviews the research status of optical diffractive neural networks in the field of neuromorphic computing. Problems of narrowing down current ID^2 NN applications are also included in this review. Finally, future research directions for ID^2 NNย are discussed, and conclusions are delivered.