NASA’s plans for space exploration include a return to the Moon to stay—boots back on the lunar surface with an orbital outpost. This station will be a launch point for voyages to destinations further away in our solar system, including journeys to the red planet Mars. To ensure success of these missions, health and performance risks associated with the unique hazards of spaceflight must be adequately controlled. These hazards—space radiation, altered gravity fields, isolation and confinement, closed environments, and distance from Earth—are linked with over 30 human health risks as documented by NASA’s Human Research Program. The programmatic goal is to develop the tools and technologies to adequately mitigate, control, or accept these risks. The risks ranked as “red” have the highest priority based on both the likelihood of occurrence and the severity of their impact on human health, performance in mission, and long-term quality of life. These include: (1) space radiation health effects of cancer, cardiovascular disease, and cognitive decrements (2) Spaceflight-Associated Neuro-ocular Syndrome (3) behavioral health and performance decrements, and (4) inadequate food and nutrition. Evaluation of the hazards and risks in terms of the space exposome—the total sum of spaceflight and lifetime exposures and how they relate to genetics and determine the whole-body outcome—will provide a comprehensive picture of risk profiles for individual astronauts. In this review, we provide a primer on these “red” risks for the research community. The aim is to inform the development of studies and projects with high potential for generating both new knowledge and technologies to assist with mitigating multisystem risks to crew health during exploratory missions.