  The development of applications based on artificial intelligence and
implemented over wireless networks is increasingly rapidly and is expected to
grow dramatically in the future. The resulting demand for the aggregation of
large amounts of data has caused serious communication bottlenecks in wireless
networks and particularly at the network edge. Over-the-air federated learning
(OTA-FL), leveraging the superposition feature of multi-access channels (MACs),
enables users at the network edge to share spectrum resources and achieves
efficient and low-latency global model aggregation. This paper provides a
holistic review of progress in OTA-FL and points to potential future research
directions. Specifically, we classify OTA-FL from the perspective of system
settings, including single-antenna OTA-FL, multi-antenna OTA-FL, and OTA-FL
with the aid of the emerging reconfigurable intelligent surface (RIS)
technology, and the contributions of existing works in these areas are
summarized. Moreover, we discuss the trust, security and privacy aspects of
OTA-FL, and highlight concerns arising from security and privacy. Finally,
challenges and potential research directions are discussed to promote the
future development of OTA-FL in terms of improving system performance,
reliability, and trustworthiness. Specifical challenges to be addressed include
model distortion under channel fading, the ineffective OTA aggregation of local
models trained on substantially unbalanced data, and the limited accessibility
and verifiability of individual local models.
