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Cancer risk estimation remains one of the main unresolved challenges in human spaceflight beyond low Earth orbit, where astronauts are exposed to galactic cosmic rays, solar particle events, and high-linear energy transfer (high-LET) secondary radiation. This narrative review summarizes the principal quantitative models used to estimate radiation-induced cancer risk in astronauts, including particle fluence-based cross-sections, mixture models, risk of exposure-induced death (REID)-based operational frameworks, uncertainty distribution approaches, and ensemble models. Early studies estimated 1-year excess cancer mortality at solar minimum as 1.3% in women and 1.1% in men under 10 g/cm² aluminum shielding, whereas later models projected non-leukemia lifetime cancer incidence after 1 Sv dose equivalent/effective dose between 2.20% and 2.98%, depending on sex and age. Earlier REID-based models suggested that the historical 3% REID threshold could be exceeded after approximately 18 months in women and 24 months in men under unfavorable solar conditions, whereas the current NASA radiation standard uses a universal career-effective dose limit of 600 mSv, applied regardless of sex or age. More recent revisions of the NASA Space Cancer Risk model and non-targeted effect scenarios suggest that exploration mission risks may be higher than previously estimated, while uncertainty remains substantial, especially for high-LET radiobiology, mixed-field exposure, and the transfer of terrestrial epidemiological data to the spaceflight setting. Future progress may also involve exploring quantitative imaging biomarkers and tomographic assessments as complementary tools for longitudinal monitoring and early detection of radiation-related tissue changes, although these approaches are not yet validated as components of operational astronaut cancer risk models.