Threats to health from climate change are increasingly recognized, yet little research into the effects upon health systems is published. However, additional demands on health systems are increasingly documented. Pathways include direct weather impacts, such as amplified heat stress, and altered ecological relationships, including alterations to the distribution and activity of pathogens and vectors. The greatest driver of demand on future health systems from climate change may be the alterations to socioeconomic systems; however, these “tertiary effects” have received less attention in the health literature. Increasing demands on health systems from climate change will impede health system capacity. Changing weather patterns and sea-level rise will reduce food production in many developing countries, thus fostering undernutrition and concomitant disease susceptibility. Associated poverty will impede people's ability to access and support health systems. Climate change will increase migration, potentially exposing migrants to endemic diseases for which they have limited resistance, transporting diseases and fostering conditions conducive to disease transmission. Specific predictions of timing and locations of migration remain elusive, hampering planning and misaligning needs and infrastructure. Food shortages, migration, falling economic activity, and failing government legitimacy following climate change are also “risk multipliers” for conflict. Injuries to combatants, undernutrition, and increased infectious disease will result. Modern conflict often sees health personnel and infrastructure deliberately targeted and disease surveillance and eradication programs obstructed. Climate change will substantially impede economic growth, reducing health system funding and limiting health system adaptation. Modern medical care may be snatched away from millions who recently obtained it.