Suppose one has a configuration of points in 3D, and one measures the distances between some of the pairs of points. Under what conditions will this distance data be sufficient to uniquely determine the point configuration (up to congruence)? I will talk about this problem in two settings. In the labeled setting, the measurement data includes the labels assigning each distance to a specific point pair. In the unlabeled setting, the data is simply a list of lengths, with no associated indexing data.