High-dimensional collections of 0-1 data occur in many applications. The attributes in such data sets are typically considered to be unordered. However, in many cases there is a natural total or partial order underlying the variables of the data set. Examples of variables for which such orders exist include terms in documents and paleontological sites in fossil data collections. We describe methods for finding fragments of total orders from such data, based on finding frequently occurring patterns. We also discuss techniques for finding good total orderings (seriation) based on spectral ordering and MCMC methods