A migraine attack is a moderate or severe headache that usually occurs on one side of the head and is often accompanied by throbbing, sensitivity to light, sensitivity to sound, nausea, or other symptoms. The main goal of the study is to see if atogepant is effective, safe, and well-tolerated in treating migraine attacks quickly. Atogepant is a medicine currently approved for the preventive treatment of migraine in adults and has been shown to be effective and well tolerated when taken daily to prevent migraine attacks. This study includes double-blind phase means that neither the participants nor the study doctors know who is given which study treatment (atogepant or placebo) followed by an open-label phase meaning that both participants and study doctors know which study treatment is given. All participants will receive atogepant during the open-label part of the study. This study will include 1300 participants aged 18-75 years with a history of migraine at approximately 160 sites across the world. All participants will receive both atogepant and placebo to treat qualifying migraines. At the start of the study, participants will be randomized to 1 of 4 dosing sequences to determine when they will receive atogepant and when they will receive placebo during the study. After treating 4 qualifying migraine attacks, participants will receive open-label atogepant for any additional migraine attacks they have until the end of the study (Week 24). There may be a bigger responsibility for participants in this study than there would be in participants receiving standard of care treatment. participants will attend regular visits during the study at a hospital or clinic, as well as telephone visits, and the effects of treatment will be checked by completion of questionnaires in an electronic diary, medical assessments, blood tests, and checking for side effects.