Analyzing massive amounts of data using complex machine learning models requires significant computational resources. The conventional approach to such problems involves centralizing training data and inference processes in the cloud, i.e., in data centers. However, with the proliferation of mobile devices and increasing application of the Internet-of-Things (IoT) paradigm, very large amounts of data are collected at the edges of wireless networks, and due to privacy constraints and limited communication resources, it is undesirable or impractical to upload this data from mobile devices to the cloud for centralized learning. This problem can be solved by distributed learning at the network edge, by which edge devices collaboratively train a shared learning model using real-time mobile data. The avoidance of raw-data uploading not only helps to preserve privacy but may also alleviate network-traffic congestion and minimize latency. With that said, distributed training still requires a substantial amount of information exchange between devices and edge servers over wireless links. In the process, wireless impairments such as noise, interference, and imperfect knowledge of channel states can significantly slow down distributed learning (e.g., convergence speed) and degrades its performance (e.g., learning accuracy). This makes it crucial to optimize wireless network performance so as to support the efficient deployment of distributed learning algorithms. On the other hand, distributed learning algorithms provide a powerful tool-set for solving complex problems in wireless communication and networking. One important framework, called federated learning (FL), enables users to collaboratively learn a shared model while helping to preserve local data privacy. The application of FL can endow edge devices with capabilities of user behavior prediction, user identification, and wireless environment analysis. As another example, distributed reinforcement learning is capable of leveraging distributed computation power and data to solve complex optimization and control problems that arise in various use cases, such as network control, user clustering, resource management, and interference alignment. To cover this paradigm of distributed learning over wireless networks, this two-part Special Issue features papers dealing with two main research challenges: a) optimization of wireless network performance for efficient implementation of distributed learning in wireless networks, and b) distributed learning for solving communication problems and optimizing network performance.