A comprehensive survey of federated transfer learning (FTL) explores its challenges, methods, and applications. Federated learning (FL) enables participants to train a centralized model without sharing data, but data and system heterogeneity, incremental data, and labeled data scarcity hinder performance. FTL integrates transfer learning (TL) into FL to address these issues by enabling knowledge transfer between domains. This survey categorizes FTL scenarios into homogeneous, heterogeneous, dynamic heterogeneous, model adaptive, semi-supervised, and unsupervised FTL. It discusses existing solutions, including data-based and model-based strategies, and outlines common settings, datasets, and applications. Challenges include prior shift, covariate shift, feature concept shift, label concept shift, and quantity shift. Solutions involve instance augmentation, instance selection, and feature clustering to improve model convergence and performance. The survey also highlights the importance of addressing system heterogeneity, incremental data, and model heterogeneity in FTL. Overall, FTL offers a promising approach to overcome the limitations of traditional FL in distributed machine learning scenarios.A comprehensive survey of federated transfer learning (FTL) explores its challenges, methods, and applications. Federated learning (FL) enables participants to train a centralized model without sharing data, but data and system heterogeneity, incremental data, and labeled data scarcity hinder performance. FTL integrates transfer learning (TL) into FL to address these issues by enabling knowledge transfer between domains. This survey categorizes FTL scenarios into homogeneous, heterogeneous, dynamic heterogeneous, model adaptive, semi-supervised, and unsupervised FTL. It discusses existing solutions, including data-based and model-based strategies, and outlines common settings, datasets, and applications. Challenges include prior shift, covariate shift, feature concept shift, label concept shift, and quantity shift. Solutions involve instance augmentation, instance selection, and feature clustering to improve model convergence and performance. The survey also highlights the importance of addressing system heterogeneity, incremental data, and model heterogeneity in FTL. Overall, FTL offers a promising approach to overcome the limitations of traditional FL in distributed machine learning scenarios.