The explosive growth of image data facilitates the fast development of image processing and computer vision methods for emerging visual applications, meanwhile introducing novel distortions to processed images. This poses a grand challenge to existing blind image quality assessment (BIQA) models, which are weak at adapting to subpopulation shift. Recent work suggests training BIQA methods on the combination of all available human-rated IQA datasets. However, this type of approach is not scalable to a large number of datasets and is cumbersome to incorporate a newly created dataset as well. In this paper, we formulate continual learning for BIQA, where a model learns continually from a stream of IQA datasets, building on what was learned from previously seen data. We first identify five desiderata in the continual setting with three criteria to quantify the prediction accuracy, plasticity, and stability, respectively. We then propose a simple yet effective continual learning method for BIQA. Specifically, based on a shared backbone network, we add a prediction head for a new dataset and enforce a regularizer to allow all prediction heads to evolve with new data while being resistant to catastrophic forgetting of old data. We compute the overall quality score by a weighted summation of predictions from all heads. Extensive experiments demonstrate the promise of the proposed continual learning method in comparison to standard training techniques for BIQA, with and without experience replay. We made the code publicly available at https://github.com/zwx8981/BIQA_CL.