In the early 1980s, DNA sequencing became a routine and the increasing computing power opened the door to reconstruct molecular phylogenies using probabilistic approaches. DNA sequence alignments provided a large number of positions containing phylogenetic information, which could be extracted using explicit statistical models that described the mutation process using appropriate parameters. Consequently, an active quest started for building increasingly improved (more realistic) statistical models of nucleotide substitution. The simplest model assumed that nucleotide frequencies were in equilibrium and one single category of substitutions. Subsequent models allowed either unequal nucleotide frequencies or separate rates for transitions and transversions. The HKY85 model (Hasegawa et al. in J Mol Evol 22:160, 1985) combined elegantly both options into a single model, which became one of the most useful ones and has been the choice in many molecular phylogenetic studies ever since. The use of improved substitution models such as HKY85 allows reconstructing more accurate and reliable phylogenies, which in turn provide robust frameworks for understanding how biological diversity evolved and for performing a wealth of comparative studies in different disciplines such as ecology, biogeography, developmental biology, biochemistry, genomics, epidemiology, and biomedicine.