The Inverse Depletion Theory (INDEPTH) code is used to reconstruct design and operating history parameters of a nuclear reactor from measurements of spent nuclear fuel. Typical parameters of interest are the initial enrichment of the fuel, the burnup, and the cooling time. These reconstructed values can be used to verify safeguards declarations, confirm that environmental samples are consistent with declared nuclear activities, or recover surveillance on spent fuel for which the history has been lost. INDEPTH uses the Oak Ridge Isotope Generation (ORIGEN) code to perform forward depletion and decay calculations and generate a set of synthetic data to compare to the inputs. INDEPTH uses a gradient-based search to adjust the reactor parameters in the ORIGEN simulations until the optimum set of parameters is found. In previous spent fuel measurements, INDEPTH was able to reconstruct burnup to within 7% of trusted operator declarations using nondestructive assay measurements, and to within 2% using destructive assay measurements. This paper presents an overview of the INDEPTH method and the results of previous reconstructions using spent fuel measurements.