Human emotions contain both basic and compound facial expressions. In many practical scenarios, it is difficult to access all the compound expression categories at one time. In this paper, we investigate comprehensive facial expression recognition (FER) in the class-incremental learning paradigm, where we define well-studied and easily-accessible basic expressions as initial classes and learn new compound expressions incrementally. To alleviate the stability-plasticity dilemma in our incremental task, we propose a novel Relationship-Guided Knowledge Transfer (RGKT) method for class-incremental FER. Specifically, we develop a multi-region feature learning (MFL) module to extract fine-grained features for capturing subtle differences in expressions. Based on the MFL module, we further design a basic expression-oriented knowledge transfer (BET) module and a compound expression-oriented knowledge transfer (CET) module, by effectively exploiting the relationship across expressions. The BET module initializes the new compound expression classifiers based on expression relevance between basic and compound expressions, improving the plasticity of our model to learn new classes. The CET module transfers expression-generic knowledge learned from new compound expressions to enrich the feature set of old expressions, facilitating the stability of our model against forgetting old classes. Extensive experiments on three facial expression databases show that our method achieves superior performance in comparison with several state-of-the-art methods.