Contrastive learning demonstrates great promise for representation learning. Data augmentations play a critical role in contrastive learning by providing informative views of the data without needing the labels. However, the performance of the existing works heavily relies on the quality of the employed data augmentation (DA) functions, which are typically hand picked from a restricted set of choices. While exploiting a diverse set of data augmentations is appealing, the intricacies of DAs and representation learning may lead to performance degradation. To address this challenge and allow for a systemic use of large numbers of data augmentations, this paper proposes Contrastive Learning with Consistent Representations (CoCor). At the core of CoCor is a new consistency measure, DA consistency, which dictates the mapping of augmented input data to the representation space such that these instances are mapped to optimal locations in a way consistent to the intensity of the DA applied. Furthermore, a data-driven approach is proposed to learn the optimal mapping locations as a function of DA while maintaining a desired monotonic property with respect to DA intensity. The proposed techniques give rise to a semi-supervised learning framework based on bi-level optimization, achieving new state-of-the-art results for image recognition.