A migraine is a moderate to severe headache on one side of the head. A migraine attack is a headache that may be accompanied by throbbing, nausea, vomiting, sensitivity to light and sound, or other symptoms. A number of treatments are available for adults with migraine but there are limited approved treatments available for participants less than 18 years of age. The main goal of the study is to evaluate the long-term safety and tolerability of atogepant in pediatric participants between the ages of 6 and 17 with migraine. Atogepant is a medicine currently approved to treat adults with migraine (0 to 14 migraine days per month) and is being studied in pediatric participants between the ages of 6 and 17 with a history of migraine. This is a Phase 3, open-label study of atogepant in participants with a history of migraine. Participants must have completed participation in another study of atogepant (lead-in study). Participants must have 4 to 14 migraine days and less than 15 headache days for episodic migraine, and \>= 15 headache days and \>= 8 migraine days for chronic migraine in the 4-week screening electronic diary (eDiary; similar to a smart phone). Around 650 participants will be enrolled in the study at approximately 100 sites worldwide. Atogepant is a tablet taken once a day by mouth. Participants between the ages of 12 and 17 will receive high dose atogepant for 52 Weeks. Participants between the ages of 6 and 11 will receive an atogepant dose determined in the lead-in study for 52 Weeks. There may be a bigger responsibility for participants in this study. Participants will attend regular visits during the study at a hospital or clinic. The effects of treatment will be checked by medical assessments, blood tests, checking for side effects, and completing questionnaires.