Motivated by the ever-increasing demands for massive data processing and intelligent data analysis at the network edge, federated learning (FL), a distributed architecture for machine learning, has been introduced to enhance edge intelligence without compromising data privacy. Nonetheless, due to the large number of edge devices (referred to as clients in FL) with only limited wireless resources, client scheduling, which chooses only a subset of devices to participate in each round of FL, becomes a more feasible option. Unfortunately, the training latency can be intolerable in the iterative process of FL. To tackle the challenge, this article introduces update-importance-based client scheduling schemes to reduce the required number of rounds. Then latency-based client scheduling schemes are proposed to shorten the time interval for each round. We consider the scenario where no prior information regarding the channel state and the resource usage of the devices is available, and propose a scheme based on the multi-armed bandit theory to strike a balance between exploration and exploitation. Finally, we propose a latency-based technique that exploits update importance to reduce the training time. Computer simulation results are presented to evaluate the convergence rate with respect to the rounds and wall-clock time consumption.