Problems related to the development of concepts of rational taxonomy and rational classifications (taxonomic systems) in biology are discussed. A rational taxonomy is based on the assumption that the key characteristic of rationality is the deductive inference of certain partial judgments about the reality under study from other judgments taken as more general and a priori true. Two forms of rationality are distinguished: ontological and epistemological. The former implies the inference of classification properties from general (essential) properties of the reality being investigated. The latter implies the inference of partial rules about classification from more general (formal) rules. The following principal concepts of ontological-rational biological taxonomy are considered: the crystallographic approach; inference of the orderliness of organism diversity from the general laws of nature; and inference of the above orderliness from the orderliness of ontogenetic development programs, based on the concept of natural kind and Cassirer’s series theory, grounded in the systemic concept and the idea of periodic systems. Various concepts of ontological-rational taxonomy can be generalized by the idea of causal taxonomy; that is, any biologically sound classification is founded on a content-based model of biological diversity that includes an explicit indication of the general causes responsible for that diversity. It is asserted that each category of general causation and respective background model may serve as a basis for a particular ontological-rational system as a distinctive research program. Concepts of epistemologically rational taxonomy and classifications (taxonomic systems) can be interpreted in terms of the application of certain epistemological criteria of substantiation of the scientific status of the taxonomy in general and of taxonomic systems in particular. These concepts include consideration of taxonomy consistency from the standpoint of inductive and hypothetic-deductive argumentation schemes; such fundamental criteria of classifications’ naturalness as their prognostic capabilities; and the foundation of a theory of “general taxonomy” as a “general logic,” including elements of the axiomatic method. The latter concept constitutes the core of the program of general classiology; it is inconsistent due to the absence of anything like general logic. It is asserted that elaboration of a theory of taxonomy as a biological discipline, based on the formal principles of epistemological rationality, is not feasible. Instead, it must be elaborated as an ontological-rational one, based on biologically sound meta-theories about the causes of biological diversity.