Abstract Functional reductionism characterises inter-theoretic reduction as the recovery of the upper-level behaviour described by the reduced theory in terms of the lower-level reducing theory. For instance, finding a statistical mechanical realiser that plays the functional role of thermodynamic entropy allows to establish a reductive link between thermodynamics and statistical mechanics. This view constitutes a unique approach to reduction that enjoys a number of positive features, but has received limited attention in the philosophy of science. This paper aims to clarify the meaning of functional reductionism in science, with a focus on physics, to define both its place with respect to other approaches to reduction and its connection to ontology. To do so, we develop and explore two alternative versions of functional reductionism, called Syntactic Functional Reductionism and Semantic Functional Reductionism, that expand and improve the basic functional reductionist approach along different lines, and make clear how the approach works in practice. The former elaborates on David Lewis’ account, is connected with the syntactic view of theories, employs a logical characterisation of functional roles, and is embedded within Nagelian reductionism. The latter adopts a semantic approach to theories, spells out functional roles mainly in terms of mathematical roles within the models, and is expressed in terms of the related structuralist approach to reduction. The development of these frameworks has the final goal of advancing functional reductionism, making it a fully developed account of reduction in science.