The space environment consists of a complex mixture of different types of ionizing radiation and altered gravity that represents a threat to humans during space missions. In particular, individual radiation sensitivity is strictly related to the risk of space radiation carcinogenesis. Therefore, in view of future missions to the Moon and Mars, there is an urgent need to estimate as accurately as possible the individual risk from space exposure to improve the safety of space exploration. In this review, we survey the combined effects from the two main physical components of the space environment, ionizing radiation and microgravity, to alter the genetics and epigenetics of human cells, considering both real and simulated space conditions. Data collected from studies on human cells are discussed for their potential use to estimate individual radiation carcinogenesis risk from space exposure.