In the last years, materializations of neuromorphic circuits based on nanophotonic arrangements have been proposed, which contain complete optical circuits, laser, photodetectors, photonic crystals, optical fibers, flat waveguides and other passive optical elements of nanostructured materials, which eliminate the time of simultaneous processing of big groups of data, taking advantage of the quantum perspective, and thus highly increasing the potentials of contemporary intelligent computational systems. This article is an effort to record and study the research that has been conducted concerning the methods of development and materialization of neuromorphic circuits of neural networks of nanophotonic arrangements. In particular, an investigative study of the methods of developing nanophotonic neuromorphic processors, their originality in neuronic architectural structure, their training methods and their optimization was realized along with the study of special issues such as optical activation functions and cost functions. The main contribution of this research work is that it is the first time in the literature that the most well-known architectures, training methods, optimization and activations functions of the nanophotonic networks are presented in a single paper. This study also includes an extensive detailed meta-review analysis of the advantages and disadvantages of nanophotonic networks.