Background While responsible innovation in health (RIH) suggests that health innovations could be purposefully designed to better support health systems, little is known about the system-level challenges that it should address. The goal of this paper is thus to document what is known about health systems’ demand for innovations. Methods We searched ۸ databases to perform a scoping review of the scientific literature on health system challenges published between January ۲۰۰۰ and April ۲۰۱۶. The challenges reported in the articles were classified using the dynamic health system framework. The countries where the studies had been conducted were grouped using the human development index (HDI). Frequency distributions and qualitative content analysis were performed. Results Up to ۱۳۹۱ challenges were extracted from ۲۵۴ articles examining health systems in ۹۹ countries. Across countries, the most frequently reported challenges pertained to: service delivery (۲۵%), human resources (۲۳%), and leadership and governance (۲۱%). Our analyses indicate that innovations tend to increase challenges associated to human resources by affecting the nature and scope of their tasks, skills and responsibilities, to exacerbate service delivery issues when they are meant to be used by highly skilled providers and call for accountable governance of their dissemination, use and reimbursement. In countries with a low and medium HDI, problems arising with infrastructure, logistics and equipment were described in connection with challenges affecting procurement, supply and distribution systems. In countries with a medium and high HDI, challenges included a growing demand for drugs and new technology and the management of rising costs. Across all HDI groups, the need for flexible information technologies (IT) solutions to reach rural areas was underscored. Conclusion Highlighting challenges that are common across countries, this study suggests that RIH should aim to reduce the cost of innovation production processes and attend not only to the requirements of the immediate clinical context of use, but also to the vulnerabilities of the broader system wherein innovations are deployed. Policy-makers should translate system-level demand signals into innovation development opportunities since it is imperative to foster innovations that contribute to the success and sustainability of health systems.