Federated Continual Learning (FCL) has emerged as a promising paradigm that combines Federated Learning (FL) and Continual Learning (CL). To achieve good model accuracy, FCL needs to tackle catastrophic forgetting due to concept drift over time in CL, and to overcome the potential interference among clients in FL. We propose Concept Matching (CM), a clustering-based framework for FCL to address these challenges. The CM framework groups the client models into concept model clusters, and then builds different global models to capture different concepts in FL over time. In each round, the server sends the global concept models to the clients. To avoid catastrophic forgetting, each client selects the concept model best-matching the concept of the current data for further fine-tuning. To avoid interference among client models with different concepts, the server clusters the models representing the same concept, aggregates the model weights in each cluster, and updates the global concept model with the cluster model of the same concept. Since the server does not know the concepts captured by the aggregated cluster models, we propose a novel server concept matching algorithm that effectively updates a global concept model with a matching cluster model. The CM framework provides flexibility to use different clustering, aggregation, and concept matching algorithms. The evaluation demonstrates that CM outperforms state-of-the-art systems and scales well with the number of clients and the model size.