Deep-learning methods for computational pathology require either manual annotation of gigapixel whole-slide images (WSIs) or large datasets of WSIs with slide-level labels and typically suffer from poor domain adaptation and interpretability. Here we report an interpretable weakly supervised deep-learning method for data-efficient WSI processing and learning that only requires slide-level labels. The method, which we named clustering-constrained-attention multiple-instance learning (CLAM), uses attention-based learning to identify subregions of high diagnostic value to accurately classify whole slides and instance-level clustering over the identified representative regions to constrain and refine the feature space. By applying CLAM to the subtyping of renal cell carcinoma and non-small-cell lung cancer as well as the detection of lymph node metastasis, we show that it can be used to localize well-known morphological features on WSIs without the need for spatial labels, that it overperforms standard weakly supervised classification algorithms and that it is adaptable to independent test cohorts, smartphone microscopy and varying tissue content.