According to the semantic view of scientific theories, theories are classes of models. I show that this view—if taken literally—leads to absurdities. In particular, this view equates theories that are distinct, and it distinguishes theories that are equivalent. Furthermore, the semantic view lacks the resources to explicate interesting theoretical relations, such as embeddability of one theory into another. The untenability of the semantic view—as currently formulated—threatens to undermine scientific structuralism.