As artificial intelligence (AI)-empowered applications become widespread, there is growing awareness and concern for user privacy and data confidentiality. This has contributed to the popularity of federated learning (FL). FL applications often face data distribution and device capability heterogeneity across data owners. This has stimulated the rapid development of Personalized FL (PFL). In this paper, we complement existing surveys, which largely focus on the methods and applications of FL, with a review of recent advances in PFL. We discuss hurdles to PFL under the current FL settings, and present a unique taxonomy dividing PFL techniques into data-based and model-based approaches. We highlight their key ideas, and envision promising future trajectories of research towards new PFL architectural design, realistic PFL benchmarking, and trustworthy PFL approaches.
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