Although various first-order and second-order algorithms have been developed to improve the training efficiency of FEEL, they are not applicable to situations where the gradient information is unavailable, such as federated black-box attacks and federated hyperparameter tuning. In this chapter, we present a derivative-free federated zeroth-order optimization (FedZO) algorithm and also provide theoretical analysis for the convergence performance of the FedZO algorithm under non-convex settings. To enhance communication efficiency of FedZO over wireless networks, we develop an AirComp assisted FedZO algorithm. By appropriately optimizing the AirComp transceiver, the convergence of the AirComp-assisted FedZO algorithm is maintained under certain signal-to-noise ratio settings. Simulation results establish the effectiveness of the FedZO algorithm and verify the theoretical findings, highlighting its potential in scenarios where gradient information is not accessible.