Neural networks (NNs) have revolutionized various fields, including aeronautics where it is applied in computational fluid dynamics, finite element analysis, load prediction, and structural optimization. Particularly in optimization, neural networks and deep neural networks are extensively employed to enhance the efficiency of genetic algorithms because, with this tool, it is possible to speed up the finite element analysis process, which will also speed up the optimization process. The main objective of this paper is to present how neural networks can help speed up the process of optimizing the geometries and composition of composite structures (dimension, topology, volume fractions, reinforcement architecture, matrix/reinforcement composition, etc.) compared to the traditional optimization methods. This article stands out by showcasing not only studies related to aeronautics but also those in the field of mechanics, emphasizing that the underlying principles are shared and applicable to both domains. The use of NNs as a surrogate model has been demonstrated to be a great tool for the optimization process; some studies have shown that the NNs are accurate in their predictions, with an MSE of $1\times {10}^{-5}$ and MAE of 0.007%. It has also been observed that its use helps to reduce optimization time, such as up to a speed 47.5 times faster than a full aeroelastic model.