Conventional machine learning techniques are conducted in a centralized manner. Recently, the massive volume of generated wireless data, the privacy concerns and the increasing computing capabilities of wireless end-devices have led to the emergence of a promising decentralized solution, termed as Wireless Federated Learning (WFL). In this first of the two parts paper, we present the application of WFL in the sixth generation of wireless networks (6G), which is envisioned to be an integrated communication and computing platform. After analyzing the key concepts of WFL, we discuss the core challenges of WFL imposed by the wireless (or mobile communication) environment. Finally, we shed light to the future directions of WFL, aiming to compose a constructive integration of FL into the future wireless networks.