Radiation therapy has been used worldwide for many decades as a therapeutic regimen for the treatment of different types of cancer. Just over 50% of cancer patients are treated with radiotherapy alone or with other types of antitumor therapy. Radiation can induce different types of cell damage: directly, it can induce DNA single- and double-strand breaks; indirectly, it can induce the formation of free radicals, which can interact with different components of cells, including the genome, promoting structural alterations. During treatment, radiosensitive tumor cells decrease their rate of cell proliferation through cell cycle arrest stimulated by DNA damage. Then, DNA repair mechanisms are turned on to alleviate the damage, but cell death mechanisms are activated if damage persists and cannot be repaired. Interestingly, some cells can evade apoptosis because genome damage triggers the cellular overactivation of some DNA repair pathways. Additionally, some surviving cells exposed to radiation may have alterations in the expression of tumor suppressor genes and oncogenes, enhancing different hallmarks of cancer, such as migration, invasion, and metastasis. The activation of these genetic pathways and other epigenetic and structural cellular changes in the irradiated cells and extracellular factors, such as the tumor microenvironment, is crucial in developing tumor radioresistance. The tumor microenvironment is largely responsible for the poor efficacy of antitumor therapy, tumor relapse, and poor prognosis observed in some patients. In this review, we describe strategies that tumor cells use to respond to radiation stress, adapt, and proliferate after radiotherapy, promoting the appearance of tumor radioresistance. Also, we discuss the clinical impact of radioresistance in patient outcomes. Knowledge of such cellular strategies could help the development of new clinical interventions, increasing the radiosensitization of tumor cells, improving the effectiveness of these therapies, and increasing the survival of patients.