<p>This article presents a review of the current state of neural network applications in plastic deformation processes, together with an experimental study and modeling of the electromagnetic forming process of AlMn0.5Mg0.5 aluminum alloy sheet. The first part summarizes several case studies that demonstrate the potential of neural networks in the plastic deformation of metallic and non-metallic materials such as composites, glasses, polymers, foams, clay, as well as shape memory alloys. This part examines different types of neural networks, learning algorithms, feature selection methods, and optimization techniques that apply to plastic deformation processes. It also explores their integration with other modeling approaches, such as regression and finite element analysis. The second part focuses on predicting the maximum deformation depth, which serves as an indicator of formability, in the electromagnetic bulging of round cups. Six process parameters (deformed part size, thickness of specimen, gap distance, number of coil turns, capacitance of capacitor bank and the charging voltage) are identified as significantly influential and serve as input variables for both the experimental design and modeling. The study applies both nonlinear regression and neural networks to predict the output parameter. Both models reliably predict the output parameter, and their performance is demonstrated by an average relative error of 2.53% for the nonlinear regression model and a coefficient of determination of 0.9971 for the neural network model, which indicate their potential for manufacturing process control.</p>