Unlike previous generations of mobile networks, the beyond 5G (B5G) network is envisioned to support edge intelligence, which is to provide both communication and computing capabilities to the proximity of end users. Wireless edge intelligence is particularly important to those crucial use cases of B5G, including smart cities, autonomous driving, wireless healthcare, virtual reality (VR) and augmented reality (AR) gaming, where mobile networks are expected to be equipped with intelligent capabilities for prediction and shaping experiences to individuals. Federated learning (FL) is a key enabling technology for wireless edge intelligence, by performing the model training in a decentralized manner and keeping the data where it is generated. However, a straightforward adaption of FL from computer networks to wireless systems can suffer performance degradation in spectral and implementation efficiency, because of the complex wireless environment with heterogeneous resources and a massive number of devices. The aim of this project is to develop a novel scalable hybrid architecture for wireless FL by efficiently utilising the physical layer dynamics of the mobile communication environments and exploiting sophisticated service-aware and resource-aware collaborative edge learning. The novelty of the project is the development of this novel edge learning architecture, where the fundamental limits of the learning architecture is characterised by advanced mathematical tools, such as graph theory and stochastic learning. In addition, an algorithmic framework for quantifying challenging design trade-offs in the presence of practical constraints by applying sophisticated tools such as compressed sensing and machine learning.