Stored red blood cells (RBCs) are needed for life-saving blood transfusions, but they undergo continuous degradation. RBC storage lesions are often assessed by microscopic examination or biochemical and biophysical assays, which are complex, time-consuming, and destructive to fragile cells. Here we demonstrate the use of label-free imaging flow cytometry and deep learning to characterize RBC lesions. Using brightfield images, a trained neural network achieved 76.7% agreement with experts in classifying seven clinically relevant RBC morphologies associated with storage lesions, comparable to 82.5% agreement between different experts. Given that human observation and classification may not optimally discern RBC quality, we went further and eliminated subjective human annotation in the training step by training a weakly supervised neural network using only storage duration times. The feature space extracted by this network revealed a chronological progression of morphological changes that better predicted blood quality, as measured by physiological hemolytic assay readouts, than the conventional expert-assessed morphology classification system. With further training and clinical testing across multiple sites, protocols, and instruments, deep learning and label-free imaging flow cytometry might be used to routinely and objectively assess RBC storage lesions. This would automate a complex protocol, minimize laboratory sample handling and preparation, and reduce the impact of procedural errors and discrepancies between facilities and blood donors. The chronology-based machine-learning approach may also improve upon humans' assessment of morphological changes in other biomedically important progressions, such as differentiation and metastasis.