This thesis explores the potential of edge devices in three applications: indoor localization, urban traffic prediction, and multi-modal representation learning. For indoor localization, we propose a reliable data transmission network and robust data processing framework by visible light communications and machine learning to enhance the intelligence of smart buildings. The urban traffic prediction proposes a dynamic spatial and temporal origin-destination feature enhanced deep network with the graph convolutional network to collaboratively learn a low-dimensional representation for each region to predict in-traffic and out-traffic for every city region simultaneously. The multi-modal representation learning proposes using dynamic contexts to uniformly model visual and linguistic causalities, introducing a novel dynamic-contexts-based similarity metric that considers the correlation of potential causes and effects to measure the relevance among images. To enhance distributed training on edge devices, we introduced a new system called Distributed Artificial Intelligence Over-the-Air (AirDAI), which involves local training on raw data and sending trained outputs, such as model parameters, from local clients back to a central server for aggregation. To aid the development of AirDAI in wireless communication networks, we suggested a general system design and an associated simulator that can be tailored based on wireless channels and system-level configurations. We also conducted experiments to confirm the effectiveness and efficiency of the proposed system design and presented an analysis of the effects of wireless environments to facilitate future implementations and updates. This thesis proposes FedForest to address the communication and computation limitations in heterogeneous edge networks, which optimizes the global network by distilling knowledge from aggregated sub-networks. The sub-network sampling process is differentiable, and the model size is used as an additional constraint to extract a new sub-network for the subsequent local optimization process. FedForest significantly reduces server-to-client communication and local device computation costs compared to conventional algorithms while maintaining performance with the benchmark Top-K sparsification method. FedForest can accelerate the deployment of large-scale deep learning models on edge devices.