Although FEEL is an effective approach for addressing the issue of isolated data islands while ensuring data privacy by keeping data local, it generates significant data traffic over wireless networks with limited radio resources. Most current studies use federated first-order optimization, which has a slow convergence rate, leading to excessive communication rounds between edge devices and the edge server. To alleviate this issue, we in this chapter present a novel over-the-air federated second-order optimization algorithm that reduces the number of communication rounds and enables low-latency global model aggregation. This method exploits the waveform superposition property of a multi-access channel to implement the distributed second-order optimization algorithm over wireless networks. The algorithmic convergence behavior shows a linear-quadratic rate with an accumulative error term in each iteration. Further, we show how to minimize the accumulated error by jointly optimizing device selection and beamforming vectors. Finally, simulations illustrate the effectiveness of the federated second-order optimization algorithm.