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The continuous flow of genomic data is creating unprecedented opportunities for the reconstruction of molecular phylogenies. Access to whole-genome data means that phylogenetic analysis can now be performed at different genomic levels, such as primary sequences and gene order, allowing for reciprocal corroboration of the results. We critically review the different kinds of phylogenomic methods currently available, paying particular attention to method reliability. Our emphasis is on methods for the analysis of primary sequences because these are the most advanced. We discuss the important issue of statistical inconsistency and show how failing to fully capture the process of sequence evolution in the underlying models leads to tree reconstruction artifacts. We suggest strategies for detecting and potentially overcoming these problems. These strategies involve the development of better models, the …