Current wireless communication systems are witnessing an explosive increase in data traffic. The current requirements of 5G include peaks of data rates in the order of tens of Gbit/s, latency in the order of 1 millisecond, and much larger number of devices communicating in the network. With the advances in the internet of things (IoT), 5G, and machine learning techniques, many IoT devices will use the data gathered to provide several important tasks, such as object detection for vehicular applications, using machine learning models over 5G and upcoming 6G networks. This use of machine learning over wireless networks uses the edge server and devices to learn in a collaborative manner a joint learning task, such as object detection in vehicular applications. To address this distributed learning over wireless networks, federated learning is a promising candidate. Federated learning is a distributed machine learning paradigm that pushes the learning and computation into the end-devices to improve communication efficiency and privacy. It trains a global objective function (learning task) using a central server and a subset of all nodes, which use their own local data to solve a local objective function, through an iterative process between the devices and the central server. Unlike other centralized and distributed machine learning techniques, federated learning is designed for scenarios in which the devices have to send a limited number of messages, the devices do not share the raw data, and are heterogeneous in the data and in the computation capabilities. Unfortunately, the state-of-the-art of federated learning is still unsuitable for wireless networks. The main limitation is that the joint investigation of federated learning and wireless communications needs is not present in the current literature, especially for devices that have low battery capacity that need to transmit high data rates in a very short time. To achieve this integration, there are still some challenges. First, federated learning algorithms must comply with the communication requirements of low latency, high reliability, high data rates and energy constraints of devices. Second, the resource allocation algorithms of wireless networks must consider the learning model and the learning task. In this project, we study the fundaments of federated learning over vehicular networks, specifically when the learning task is on vehicular applications, such as object detection. We consider a system operating in a realistic cellular environment with many antennas at the server and single-antenna vehicles. We model the system such that the communication requirements are included in the theoretical formulation. We analyse the convergence of the proposed learning method when fulfilling such requirements. We formulate a mathematical problem to maximize the speed of convergence while considering the communication requirements, the vehicles that participate in the training, the number of communication resources to be assigned, and the transmit power of each vehicle. The formulated problem is very complex, so we propose a suboptimal solution. Using our proposed solution, we intend to analyse complicated scenarios, such as more antennas, vehicles, and bigger datasets, in an efficient manner.