The goal of this thesis is to develop a learning framework for solving resource allocation problems in wireless systems. Resource allocation problems are as widespread as they are challenging to solve, in part due to the limitations in finding accurate models for these complex systems. While both exact and heuristic approaches have been developed for select problems of interest, as these systems grow in complexity to support applications in Internet of Things and autonomous behavior, it becomes necessary to have a more generic solution framework. The use of statistical machine learning is a natural choice not only in its ability to develop solutions without reliance on models, but also due to the fact that a resource allocation problem takes the form of a statistical regression problem. The second and third chapters of this thesis begin by presenting initial applications of machine learning ideas to solve problems in wireless control systems. Wireless control systems are a particular class of resource allocation problems that are a fundamental element of IoT applications. In Chapter 2, we consider the setting of controlling plants over non-stationary wireless channels. We draw a connection between the resource allocation problem and empirical risk minimization to develop convex optimization algorithms that can adapt to non-stationarities in the wireless channel. In Chapter 3, we consider the setting of controlling plants over a latency-constrained wireless channel. For this application, we utilize ideas of control-awareness in wireless scheduling to derive an assignment problem to determine optimal, latency-aware schedules. The core framework of the thesis is then presented in the fourth and fifth chapters. In Chapter 4, we formally draw a connection between a generic class of wireless resource allocation problems and constrained statistical learning, or regression. From here, this inspires the use of machine learning models to parameterize the resource allocation problem. To train the parameters of the learning model, we first establish a bounded duality gap result of the constrained optimization problem, and subsequently present a primal-dual learning algorithm. While any learning parameterization can be used, in this thesis we focus our attention on deep neural networks (DNNs). While fully connected networks can be represent many functions, they are impractical to train for large scale systems. In Chapter 5, we tackle the parallel problem in our wireless framework of developing particular learning parameterizations, or deep learning architectures, that are well suited for representing wireless resource allocation policies. Due to the graph structure inherent in wireless networks, we propose the use of graph convolutional neural networks to parameterize the resource allocation policies. Before concluding remarks and future work, in Chapter 6 we present initial results on applying the learning framework of the previous two chapters in the setting of scheduling transmissions for low-latency wireless control systems. We formulate a control-aware scheduling problem that takes the form of the constrained learning problem and apply the primal-dual learning algorithm to train the graph neural network.