The goal of the present review was to analyse the application of blockchain to support medical imaging data sharing across multiple healthcare institutions. The review included thirty-three studies that aimed to use blockchain to provide (i) authentication mechanisms, (ii) trusted communication channels, (iii) distributed mechanisms for securing the privacy for both storage and sharing of medical images, and (iv) federated machine learning algorithms. Despite these potential applications, the current research does not present effective use of blockchain in clinical settings to support medical imaging data sharing across multiple healthcare institutions.