Recently significant initiatives have been launched for the dissemination of Open Access as part of the Open Science movement. Nevertheless, two other major pillars of Open Science such as Open Research Data (ORD) and Open Peer Review (OPR) are still in an early stage of development among the communities of researchers and stakeholders. The present study sought to unveil the perceptions of a medical and health sciences community about these issues. Through the investigation of researchers’ attitudes, valuable conclusions can be drawn, especially in the field of medicine and health sciences, where an explosive growth of scientific publishing exists. A quantitative survey was conducted based on a structured questionnaire, with 179 valid responses. The participants in the survey agreed with the Open Peer Review principles. However, they ignored basic terms like FAIR (Findable, Accessible, Interoperable, and Reusable) and appeared incentivized to permit the exploitation of their data. Regarding Open Peer Review (OPR), participants expressed their agreement, implying their support for a trustworthy evaluation system. Conclusively, researchers need to receive proper training for both Open Research Data principles and Open Peer Review processes which combined with a reformed evaluation system will enable them to take full advantage of the opportunities that arise from the new scholarly publishing and communication landscape.