Differential cross section measurement in experimental particle physics are smeared by the finite resolution of particle detectors. Using the smeared observations to infer the true particle-level spectrum is an ill-posed inverse problem, which is typically referred to as unfolding or unsmearing. In this talk, I will first give an overview of the statistical techniques that are currently used for unfolding particle spectra. I will then explain how optimal point estimation and optimal uncertainty quantification are distinct and separate problems in unfolding and demonstrate that some existing unfolding methods may produce statistical uncertainties that seriously underestimate the true uncertainty. I will then describe how debiasing and shape constraints provide two complementary ways of obtaining more realistic unfolded uncertainties and discuss directions for future progress on this fundamentally challenging problem.