Purely combinatorial algorithms for comparing genomes are essentially model-free, requiring no a priori quantitative characterization of the processes of genome rearrangement. It is possible to introduce various parameters into the optimizing criterion to increase realism, but this leads to algorithmically much harder problems. Nevertheless, with the advent of eukaryotic genome sequences, answers to the following questions could aid in reconstructing the details of genomic evolution. With what frequency does each type of rearrangement operation occur in a given evolutionary lineage? What regions or sites on the chromosome are susceptible to a particular type of change? How large is the DNA segment inverted, transposed, deleted, translocated, or duplicated? Partial answers are now known for several lineages and we discuss how to integrate this information into inference about evolutionary genomics.