As artificial intelligence and deep learning becomes more important, new approaches for photonic neural computing arise. We investigate the concept of deep diffractive neural networks. First proposed in 2018, deep diffractive neural network operate passively, using coherent images and diffractive optics to do image-to-image regression and object classification. In this article we shortly review current approaches, give a brief introduction into the mathematical description of such diffractive networks using the Angular Spectrum method and show the first results of our own developments of convolutional diffractive networks with an experimental accuracy of approximately 84 %. The objective of this article is to give an introduction into the field of optical computing with neural networks using diffraction and free-space propagation of light.