As climate change impacts intensify worldwide, assessing climate risks comprehensively is essential for guiding effective disaster risk management and adaptation strategies. This systematic literature review examines the latest developments in Climate Risk Assessment (CRA), focusing on how climate risks are framed and assessed. It explores advancements, ongoing challenges, and emerging opportunities to guide future generations of CRAs. Key findings highlight a more nuanced risk framework that incorporates climate responses, modulating the three risk determinants (exposure, vulnerability, and hazards), as outlined in the latest IPCC assessment. The state-of-the-art concentrates on the temporal and spatial characteristics of hazards, while exposure and vulnerability are increasingly understood as dynamic concepts influenced by socioeconomic changes. Recent developments, such as multi-hazard approaches, risk tolerance integration, and the concept of Climatic Impact-Drivers (CID), provide new perspectives on assessing climate risks. However, managing complexity and uncertainty remain the main operational challenges, underscoring the need for improved CRA methodologies and models, as well as consistent, interoperable datasets. The paper discusses avenues to advance CRA, emphasizing the importance of bridging the gap between academic advancements and practical implementation. Conceptual recommendations include adopting a systemic approach to, for example, better account for the cascading and compounding risks, hazard thresholds, adaptation limits, and risk amplifiers, as well as using storylines to improve CRA communication. Technical recommendations include leveraging emerging technologies such as artificial intelligence, machine learning methods and big data analytics to improve real-time risk prediction and modeling. To enhance the CRA practice, the study advocates for greater stakeholder involvement and inclusive governance to ensure that CRAs remain context-specific and relevant. These recommendations, together with strengthened interdisciplinary collaboration and knowledge-sharing, are expected to pave the way for more effective climate risk management, adaptation, and resilience-building strategies.