Biological diversity (BD) explored by the biological systematics is a complexly organized natural phenomenon and can be partitioned in several aspects defined with references to various causal factors structuring biota. These BD aspects are studied by particular research programs based on specific taxonomic theories (TT). They provide in total a framework for comprehending the structure of the biological systematics and its multi-aspect relations to other fields of biology. General principles of individualizing BD aspects and construing TT as quasi-axiomatics are briefly considered. It stressed that each TT is characterized by a specific combination of interrelated ontological and epistemological premises most adequate to the BD aspect a TT deals with. The following contemporary research programs in systematics are recognized and characterized in brief: phenetic, rational (with several subprograms), numerical, typological (with several subprograms), biosystematic, biomorphic, phylogenetic (with several subprograms), evo-devo. From a scientific pluralism perspective, all these research programs related to particular naturally defined BD aspects are of the same biological and scientific significance and no one of them can pretend to take a privileged position. They elaborate “locally” natural classifications that can be united by a kind of generalized faceted classification.