Inverse problems are the most important mathematical problems in science and mathematics because they provide information about factors that are difficult to study directly. In particular, inverse problems for neutral degenerate differential equations are essential for the accurate modeling and simulation of complex systems with inherent delays and degeneracy, which have been found to have applications in various areas. The main focus of this talk is to discuss an inverse problem for a neutral degenerate differential equation in a Banach space using two approaches: one for regular data and another for irregular data. For regular data, we use the direct approach using the Volterra integral equation, and for irregular data, we use an optimal control approach. In the optimal control approach, under certain hypotheses, the characterization of the limit of the sequence of approximate solutions demonstrates that it is the solution of the original inverse problem.