There are global movements aiming to promote reform of the traditional research evaluation and reward systems. However, a comprehensive picture of the existing best practices and efforts across various institutions to integrate Open Science into these frameworks remains underdeveloped and not fully known. The aim of this study was to identify perceptions and expectations of various research communities worldwide regarding how Open Science activities are (or should be) formally recognised and rewarded. To achieve this, a global survey was conducted in the framework of the Research Data Alliance, recruiting 230 participants from five continents and 37 countries. Despite most participants reporting that their organisation had one form or another of formal Open Science policies, the majority indicated that their organisation lacks any initiative or tool that provides specific credits or rewards for Open Science activities. However, researchers from France, the United States, the Netherlands and Finland affirmed having such mechanisms in place. The study found that, among various Open Science activities, Open or FAIR data management and sharing stood out as especially deserving of explicit recognition and credit. Open Science indicators in research evaluation and/or career progression processes emerged as the most preferred type of reward.