  Facing the upcoming era of Internet-of-Things and connected intelligence,
efficient information processing, computation, and communication design becomes
a key challenge in large-scale intelligent systems. Recently, Over-the-Air
(OtA) computation has been proposed for data aggregation and distributed
computation of functions over a large set of network nodes. Theoretical
foundations for this concept exist for a long time, but it was mainly
investigated within the context of wireless sensor networks. There are still
many open questions when applying OtA computation in different types of
distributed systems where modern wireless communication technology is applied.
In this article, we provide a comprehensive overview of the OtA computation
principle and its applications in distributed learning, control, and inference
systems, for both server-coordinated and fully decentralized architectures.
Particularly, we highlight the importance of the statistical heterogeneity of
data and wireless channels, the temporal evolution of model updates, and the
choice of performance metrics, for the communication design in OtA federated
learning (FL) systems. Several key challenges in privacy, security, and
robustness aspects of OtA FL are also identified for further investigation.
