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Phylogenetic trees describe the evolutionary history among various organisms. Studies on such trees have provided many valuable insights into a host of issues in biology, ecology, and medicine, and promise even more. As we enter the second decade of the post genomic era the enormous amount of genomic sequence information available provides us with an unprecedented opportunity for inferring novel phylogenetic trees that promise extensive implications for the future. The talk describes recent developments of computational problems for model-based approaches for invoking gene duplications, surveys the frontier line of computational problems that are based on the gene tree parsimony approach, and presents software that implements algorithms for the problems faced in this field. In conclusion future directions for invoking evolutionary phenomena will be addressed.