Draft de novo genome assemblies are now available for many organisms. These assemblies are point estimates of the true genome sequences. Each is a specific hypothesis, drawn from among many alternative hypotheses, of the sequence of a genome. Assembly uncertainty, the inability to distinguish between multiple alternative assembly hypotheses, can be due to real variation between copies of the genome in the sample, errors and ambiguities in the sequenced data and assumptions and heuristics of the assemblers. Most assemblers select a single assembly according to ad hoc criteria, and do not yet report and quantify the uncertainty of their outputs. Those assemblers that do report uncertainty take different approaches to describing multiple assembly hypotheses and the support for each.