Whole genome duplication has played a major role in the evolution of many eukaryotic lineages. Polyploidy has long been postulated as a powerful mechanism for evolutionary innovation, and recent analyses have provided convincing evidence that independent ancient genome duplications occurred in the ancestors of yeast, plants, vertebrates and fish. It is the growing availability of whole genome sequences that has facilitated the detection and analysis of these polyploidizations. However, because polyploidy is often followed by massive gene loss and chromosomal rearrangements, identifying such events is not always easy. Here is presented a review of a wide array of computational methods of ever-increasing sophistication developed to identify the obscured traces of ancient polyploidy events in genomic sequences. These methods use a variety of analytical approaches, including comparative genomics, phylogenetics and molecular clock analyses. We have also reviewed recent research on the long-term evolution of genes and genomes duplicated by polyploidization. This has emerged as a fruitful field, utilizing genome-wide functional information and genomic sequence data to further our understanding of the impact of polyploidy on organismal biology and evolution.