Global crises and growing public scrutiny are prompting research systems to demonstrate how they contribute to societal well-being, not just academic excellence. This white paper from the CoARA Towards Transformations Societal Impact subgroup argues that societal impact should be a core dimension of research assessment, culture, and funding. Drawing on literature, existing national and institutional frameworks, and the experience of more than twenty members across countries and disciplines, we clarify key terms, map current approaches, and propose practical ways forward. We define societal impacts as the evidenced contributions of research to improvements beyond academia and examine why these impacts are challenging to plan for, document, and evaluate in a fair manner. We review how funders and organisations are designing calls, impact planning tools, and evaluation methods, and how these shape incentives for engagement and co-creation with societal knowledge partners. Building on this analysis, we outline six guiding principles for integrating societal impact into assessment, as well as three system enablers related to capabilities, research ecosystems, and iterative learning. For funders, institutions, evaluators, and researchers, we provide role-specific recommendations that balance accountability with learning, protecting academic freedom, research diversity, and fostering long-term, transformative change. The paper aims to support CoARA members and the wider research community in aligning reforms and building a shared, plural understanding of research value. The paper contributes to the CoARA Commitment No. 1, Recognize the diversity of contributions to, and careers in, research in accordance with the needs and nature of the research, and No. 2, Base research assessment primarily on qualitative evaluation for which peer review is central, supported by responsible use of quantitative indicators.