Computation and machine learning hold tremendous potential to improve the quality and capabilities of imaging methods used across science, medicine, engineering, and art. Despite their impressive performance on benchmark datasets, however, deep learning methods are known to behave unpredictably on some real-world data, which limits their trusted adoption in safety-critical domains. Accordingly, in this talk I will describe white-box, interpretable methods for photorealistic volumetric reconstruction that match or exceed the performance of black-box neural alternatives. I will also present recent theoretical results that guarantee correct and efficient reconstruction using our white-box approach in nonlinear computed tomography.