This paper argues that biological species should be construed as abstract models, rather than biological or even tangible entities. Various (phenetic, cladistic, biological etc.) species concepts are defined as set-theoretic models of formal theories, and their logical connections are illustrated. In this view organisms relate to a species not as instantiations, members, or mereological parts, but rather as phenomena to be represented by the model/species. This sheds new light on the long-standing problems of species and suggests their connection to broader philosophical topics such as model selection, scientific representation, and scientific realism