Purpose: Accurate segmentation of lung and infection in COVID-19 CT scans plays an important role in the quantitative management of patients. Most of the existing studies are based on large and private annotated datasets that are impractical to obtain from a single institution, especially when radiologists are busy fighting the coronavirus disease. Furthermore, it is hard to compare current COVID-19 CT segmentation methods as they are developed on different datasets, trained in different settings, and evaluated with different metrics. Methods: To promote the development of data-efficient deep learning methods, in this paper, we built three benchmarks for lung and infection segmentation based on 70 annotated COVID-19 cases, which contain current active research areas, e.g., few-shot learning, domain generalization, and knowledge transfer. For a fair comparison among different segmentation methods, we also provide standard training, validation and testing splits, evaluation metrics and, the corresponding code. Results: Based on the state-of-the-art network, we provide more than 40 pre-trained baseline models, which not only serve as out-of-the-box segmentation tools but also save computational time for researchers who are interested in COVID-19 lung and infection segmentation. We achieve average Dice Similarity Coefficient (DSC) scores of 97.3\%, 97.7\%, and 67.3\% and average Normalized Surface Dice (NSD) scores of 90.6\%, 91.4\%, and 70.0\% for left lung, right lung, and infection, respectively. Conclusions: To the best of our knowledge, this work presents the first data-efficient learning benchmark for medical image segmentation and the largest number of pre-trained models up to now. All these resources are publicly available, and our work lays the foundation for promoting the development of deep learning methods for efficient COVID-19 CT segmentation with limited data.