In this paper we clarify how ‘epistemic’ (ESR) and ‘ontic’ structural realism (OSR) should be understood and reply to some important criticisms of the latter. We shall begin with an outline of the historical origins of what might broadly be called the ‘structuralist tendency’ within philosophy of science. This has come to be identified with a form of ‘structural realism’ but it should be noted that it also includes those who adopt an anti-realist or empiricist stance. Because of the width of its embrace and its complex history, defining what is meant by ‘structure’ and characterising the tendency in general, is problematic. However, we begin by pointing out that the structuralist tendency always involves a shift in focus away from objects – however they are metaphysically conceived – to the structures in which they are (supposedly) embedded (where the reason for the qualifier ‘supposedly’ will become clear shortly). This is vague but the tendency, both historically and in its current incarnation, is not monolithic but rather includes various overlapping subgroups of structuralists.