The rewards, incentives, and recognition systems of research have profound influence over the ways in which research is conceived, conducted, disseminated, communicated, and used. They affect the behaviours and career pathways of all members of the research community and are therefore intrinsically linked to research cultures. Researchers, research services, and other community members at Research Funding and Performing Organisations (herein referred to as research organisations) play a key role in establishing recognition systems through the research assessment processes that they implement, and the criteria and weightings that they use. These recognition systems, thus, strongly contribute to determining what is understood as research quality and excellence, which are common high-level targets of assessments around the global but remain inherently hard to define. At a time when many organisations and initiatives are discussing and setting-up actions to change the way research, researchers, and research institutes are assessed, this Science Europe Paper sets out a vision for future recognition systems and offers a collection of recommendations aimed at research organisations, and good practice examples that provide examples of possible directions for change at institutional level. The recommendations presented herein are particularly timely in relation to the launch of the Coalition for Advancing Research Assessment (CoARA), and other major initiatives that are aiming for the systemic reform of research assessment systems.