The properties of a linear multiplet in interaction with supergravity and matter are presented, with a special emphasis on the coupling of Chern-Simons forms, relevant for the problem of the chiral and conformal anomalies in relation with Kaehler transformations and the corresponding anomaly cancellations. The linear supermultiplet describes an antisymmetric tensor gauge field together with a dilaton and a Majorana spinor. In particular, these fields are found among the massless modes of superstring theories. The general properties of this supermultiplet is reviewed in the Kaehler superspace formalism and the complete supersymmetric action is constructed. This includes the classically Kaehler invariant component field action for all the kinetic terms as well as a Green-Schwarz type action which exhibits a non-holomorphic gauge coupling function. (author) 32 refs.