Internet of Things (IoT) networks include smart devices that contain many sensors that allow them to interact with the physical world, collecting and processing streaming data in real time. The total energy-consumption and cost of these sensors affect the energy-consumption and the cost of IoT devices. The type of sensor determines the accuracy of the analog interface and the resolution of the analog-to-digital converters (ADCs). The ADC resolution requirement has a trade-off between sensing performance and energy consumption since the energy consumption of ADCs strongly depends on the number of bits used to represent digital samples. In this thesis, we present an energy-efficient distributed learning framework using coarsely quantized signals for IoT networks. In particular, we develop a distributed quantization-aware least-mean square (DQA-LMS) and a distributed quantization-aware recursive least-squares (DQA-RLS) algorithms that can learn parameters in an energy-efficient fashion using signals quantized with few bits while requiring a low computational cost. Moreover, we develop a bias compensation strategy to further improve the performance of the proposed algorithms. We then carry out a statistical analysis of the proposed algorithms along with a computational complexity evaluation of the proposed and existing techniques. Numerical results assess the distributed quantization-aware algorithms against existing techniques for distributed parameter estimation where IoT devices operate in a peer-to-peer mode. We also introduce an energy-efficient federated learning framework using coarsely quantized signals for IoT networks, where IoT devices exchange their estimates with a server. We then develop the quantization-aware federated averaging LMS (QA-FedAvg-LMS) algorithm to perform parameter estimation at the clients and servers. Furthermore, we devise a bias compensation strategy for QA-FedAvg-LMS, carry out its statistical analysis, and assess its performance against existing techniques with numerical results.