Molecular structure is eminently modular and expresses complexity at different levels of molecular organization (Caetano-Anolles et al., 2009). At high levels, evolutionary change occurs at extraordinary slow pace. A new protein fold can take millions of years to materialize in sequence space while new sequences develop in less than microseconds. Structural cores are generally orders of magnitude more conserved than sequences. Consequently, they carry durable phylogenetic information useful for deep exploration of biological history. Unfortunately, the complexities of structural alignments, in which similarities of two sets of atoms with unknown correspondences are sought with no restriction on the correspondences, make global phylogenetic analysis of structure an enormous bioinformational challenge (Taylor, 2007). In recent years, however, a shift of focus from molecules to molecular repertoires, advances in bioinformatics implementations, and an expanded census of structure and function provided new avenues of evolutionary exploration. Developments include: (i) the almost complete experimental acquisition of protein folds structures (∼1,200 out of 1,500 expected; Levitt, 2009) and wide coverage of the modern RNA world (Leontis et al., 2006); (ii) functional ontologies with the potential to unify biological knowledge [e.g., gene ontology, (GO); Ashburner et al., 2000]; (iii) widespread and robust assignment of known structures to genomic sequences (Chothia and Gough, 2009); and (iv) the development of phylogenomic methods that embed structure and function directly into phylogenetic analysis (Caetano-Anolles et al., 2009). Genomic abundances derived from structural and functional censuses have been used to build trees of proteomes (ToPs; Gerstein, 1998), trees of domains (ToDs; Caetano-Anolles and Caetano-Anolles, 2003), and trees of functions (ToFs; Kim and Caetano-Anolles, 2010). While the branches of ToPs encase proteomic history and resemble traditional “trees of species” built by systematic biologists, ToDs describe how components of the system (domains in proteomes) change as the entire system evolves. These rooted phylogenomic trees establish an “evolutionary arrow,” without resorting to outgroup hypotheses, defining a chronology of architectural innovation (Figure (Figure1A).1A). Trees are not phenetic statements. While they are built from multistate or quantitative valued characters, speciation in trees fulfills a molecular clock that is compatible with paleobiology and the geological record (Wang et al., 2011). In sharp contrast to standard phylogenetic methods that generate trees of genes and genomes (ToGs) from the occurrence of genomic features (e.g., nucleotides or amino acid residues in sequence sites, presence/absence of a gene), ToDs and ToPs reap the benefit of processes occurring at higher and more conserved levels of the structural hierarchy that are responsible for the accumulation of modules in biology (Caetano-Anolles et al., 2010; Mittenthal et al., 2012). The systematic study of “abundance” of molecular parts rather than their “occurrence” offers several advantages over ToGs and standard phylogenetic analysis of sequence that we here highlight: