This paper explores the possibility of extending the capa-bility of pre-trained neural image compressors (e.g., adapting to new data or target bitrates) without breaking back-ward compatibility, the ability to decode bitstreams encoded by the original model. We refer to this problem as continual learning of image compression. Our initial findings show that baseline solutions, such as end-to-end fine-tuning, do not preserve the desired backward compatibility. To tackle this, we propose a knowledge replay training strategy that effectively addresses this issue. We also design a new model architecture that enables more effective continual learning than existing baselines. Experiments are conducted for two scenarios: data-incremental learning and rate-incremental learning. The main conclusion of this paper is that neural image compressors can be fine-tuned to achieve better per-formance (compared to their pre-trained version) on new data and rates without compromising backward compati-bility. The code is publicly available online.