The Euclidean distance geometry (EDG) problem concerns the reconstruction of point configurations in R^n from prior partial knowledge of pairwise inter-point distances, often accompanied by assumptions on the prior being noisy, incomplete or unlabeled. Instances of this problem appear across diverse domains, including dimensionality reduction techniques in machine learning, predicting molecular conformations in computational chemistry, and sensor network localization for acoustic vision. This talk provides a concise (inexhaustive) overview of the typical priors that arise in EDG problems. We will then turn to a specific instance motivated by Cryo-Electron Microscopy (cryo-EM), where recovering the 3-dimensional structure of proteins can be reformulated as an EDG problem with partially labeled distances. For this problem, we will outline a generic recovery result and present a recovery algorithm that is polynomial-time in fixed dimension. The algorithm achieves exact recovery when distances are noiseless and is robust to small levels of noise.