Biological organisms are the result of a long evolutionary history, and knowledge of the path they have followed through time is very beneficial to the understanding of their extant shapes and functions. Interestingly, each lineage keeps a record of its own evolutionary history. Comparing lineages thus allows to restore the information of ancestral traits (e.g., morphologies, molecules, etc.) and gives insights on organisms living in the past, as well as on the history of their diversification. We survey mathematical models and computational methods used to reconstruct ancestral states for different levels of organization: phenotypic traits, DNA and protein sequences, gene repertoires, and genome architecture. We discuss the possibility of reconstructing ancestral genomes in their entirety, integrating all these levels of complexity.