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Federated learning is promising in enabling large-scale machine learning by massive clients without exposing their raw data. It can not only enable the clients to preserve the privacy information, but also achieve high learning performance. Existing works of federated learning mainly focus on improving learning performance in terms of model accuracy and learning task completion time. However, in practice, clients are reluctant to participate in the learning process without receiving compensation. Therefore, how to effectively motivate the clients to actively and reliably participate in federated learning is paramount. As compared to the current incentive mechanism design in other fields, such as crowdsourcing, cloud computing, smart grid, etc., the incentive mechanism for federated learning is more challenging. First, it is hard to evaluate the training data value of each client. Second, it is difficult to model the learning performance of different federated learning algorithms. In this paper, we survey the incentive mechanism design for federated learning. In particular, we present a taxonomy of existing incentive mechanisms for federated learning, which are subsequently discussed in depth by comparing and contrasting different approaches. Finally, some future directions of how to incentivize clients in federated learning have been discussed.