Phylogenetic systematics, especially involving molecular data, has had a remarkable impact on systematic biology. Numerous tree-building computer programs exist for the reconstruction of phylogenies, and many packages are available for analysis of population genetic data for estimating genetic divergence within and among populations. These advances have come about through the joining of statistical algorithms, computer programs, and DNA base-pair sequence and fragment data. Deeper genomic data are on the horizon for use with similar questions, and the next several years will witness many spectacular genetic advances. While great progress is being made on analytical approaches with molecular data in systematics, the use of the results of these analyses in biological classification has solidified into a dogmatic view, which has impeded further progress. Emphasis still remains on using only synapomorphies, even single characters, for delimitation of groups, on insisting that sister groups should have the same rank, and admitting only holophyletic (= monophyletic s. str.) groups. Evolutionary divergence within lineages and reticulate evolution are often ignored. As a result of these processes, paraphyletic groups, i.e., monophyletic groups that do not contain all descendants from a common ancestor, are often rejected. Evolutionary systematics takes the processes of descent and modification into consideration for reconstructing phylogenetic relationships involving many dimensions. This symposium presents various approaches for recognizing cladogenetic, anagenetic, and reticulate evolution in different organisms, which help reveal micro- and macro-evolutionary processes. Controversy still exists regarding how taxonomists should incorporate the diversity of evolutionary patterns and processes into biological classification. Case studies demonstrate that purely phylogenetic (cladistic) concepts of classification are unsatisfactory in cases of non-hierarchical relationships. Contributions also deal with the controversial question of recognition of paraphyletic groups in classification.