Whole-genome sequencing of many species has presented us with the opportunity to deduce the evolutionary relationships between each and every nucleotide. In this talk, I will present algorithms for this problem, which is that of multiple whole-genome alignment. The sensitivity of whole-genome alignments to parameter values can be ascertained through the use of alignment polytopes, which will be explained. I will also show how whole-genome alignments are used in comparative genomics, including the identification of novel genes, the location of micro-RNA targets, and the elucidation of cis- regulatory element and splicing signal evolution.