Semantic realism can be characterised as the idea that scientic theories are truth-bearers, and that they are true or false in virtue of the world. This notion is often assumed, but rarely discussed in the literature. I examine how it fares in the context of the semantic view of theories and in connection with the literature on scientic representation. Making sense of semantic realism requires specifying the conditions of application of theoretical models, even for models that are not actually used, which leads to several diculties. My conclusion is that semantic realism is far more demanding than one would expect. Finally, I briey examine some pragmatist alternatives.