Privacy in magnetic resonance imaging (MRI) plays an important role due to violations occurring in scanning, storing, transferring, analyzing, and sharing. This paper reviews privacy concerns in MRI and especially Brain MRI in terms of datasets, models, platforms, violations, solutions used in privacy and security in the literature, discusses important issues based on risks, techniques, policies, rules, and existing and missing points in MRIs. Even if there have been rules, regulations, policies, and laws available for preserving privacy with the available techniques anonymization, differential privacy, federated learning, pseudonymization, synthetic data generation, privacy-utility or anonymization-utility dilemma is still on novel privacy-enhancing, or preserving techniques are always required to handle sensitive data with care. This paper focuses on these issues with some suggestions, and also discusses these issues for future directions.