This work deals with the use of emerging deep learning techniques in future wireless communication networks. It will be shown that data-driven approaches should not replace, but rather complement traditional design techniques based on mathematical models. Extensive motivation is given for why deep learning based on artificial neural networks will be an indispensable tool for the design and operation of future wireless communications networks, and our vision of how artificial neural networks should be integrated into the architecture of future wireless communication networks is presented. A thorough description of deep learning methodologies is provided, starting with the general machine learning paradigm, followed by a more in-depth discussion about deep learning and artificial neural networks, covering the most widely-used artificial neural network architectures and their training methods. Deep learning will also be connected to other major learning frameworks such as reinforcement learning and transfer learning. A thorough survey of the literature on deep learning for wireless communication networks is provided, followed by a detailed description of several novel case-studies wherein the use of deep learning proves extremely useful for network design. For each case-study, it will be shown how the use of (even approximate) mathematical models can significantly reduce the amount of live data that needs to be acquired/measured to implement data-driven approaches. For each application, the merits of the proposed approaches will be demonstrated by a numerical analysis in which the implementation and training of the artificial neural network used to solve the problem is discussed. Finally, concluding remarks describe those that in our opinion are the major directions for future research in this field.