In light of the increasing frequency and intensity of natural phenomena, whether climatic or telluric, the relevance of multi-risk assessment approaches has become an important issue for understanding and estimating the impacts of disasters on complex socioeconomic systems. Two aspects contribute to the worsening of this situation. First, climate change has heightened the incidence and, in conjunction, the seriousness of geohazards that often occur with each other. Second, the complexity of these impacts on societies is drastically exacerbated by the interconnections between urban areas, industrial sites, power or water networks, and vulnerable ecosystems. In front of the recent research on this problem, and the necessity to figure out the best scientific positioning to address it, we propose, through this review analysis, to revisit existing literature on multi-risk assessment methodologies. By this means, we emphasize the new recent research frameworks able to produce determinant advances. Our selection corpus identifies pertinent scientific publications from various sources, including personal bibliographic databases, but also OpenAlex outputs and Web of Science contents. We evaluated these works from different criteria and key findings, using indicators inspired by the PRISMA bibliometric method. Through this comprehensive analysis of recent advances in multi-risk assessment approaches, we highlight main issues that the scientific community should address in the coming years, we identify the different kinds of geohazards concerned, the way to integrate them in a multi-risk approach, and the characteristics of the presented case studies. The results underscore the urgency of developing robust, adaptable methodologies, effectively able to capture the complexities of multi-risk scenarios. This challenge should be at the basis of the keys and solutions contributing to more resilient socioeconomic systems