  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.
