There are currently more than 600 bacterial species and 28 vertebrate species, ranging from primates to fishes, for which we know (nearly) their entire DNA sequences. These number will continue to increase rapidly over the next few years. Comparing these genome sequences has emerged as one of the most important areas of computational biology. For example, one way to predict functional portions of the human genome is to search among related genomes for sequences that appear to be remarkably similar due to purifying selection. I will discuss and demonstrate some of the methods and tools for such an approach, as well as some of the challenges and unsolved problems.