While deep generative models are showing exciting abilities in computer vision and natural language processing, their adoption in communication frameworks is still far underestimated. These methods are demonstrated to evolve solutions to classic communication problems such as denoising, restoration, or compression. Nevertheless, generative models can unveil their real potential in semantic communication frameworks, in which the receiver is not asked to recover the sequence of bits used to encode the transmitted (semantic) message, but only to regenerate content that is semantically consistent with the transmitted message. Disclosing generative models capabilities in semantic communication paves the way for a paradigm shift with respect to conventional communication systems, which has great potential to reduce the amount of data traffic and offers a revolutionary versatility to novel tasks and applications that were not even conceivable a few years ago. In this paper, we present a unified perspective of deep generative models in semantic communication and we unveil their revolutionary role in future communication frameworks, enabling emerging applications and tasks. Finally, we analyze the challenges and opportunities to face to develop generative models specifically tailored for communication systems.