Nonsteroidal anti-inflammatory drugs (NSAIDs) have been the first-line choice for the acute treatment of migraine attacks for decades; however, the safety of a particular NSAID is related to its treatment dose, duration, and mechanism of action. Although adverse event (AE) risks differ substantially among individual migraine treatments, increased or prolonged exposure to any NSAID elevates risks and severity of AEs. For this narrative review, we conducted a literature search of PubMed until July 2022, focusing on the history, mechanism of action, and treatment guidelines informing the safety and efficacy of celecoxib oral solution for the acute treatment of migraine attacks. Here we discuss the mechanisms of action of nonselective NSAIDs vs. cyclooxygenase-2 (COX-2) inhibitors, and how these mechanisms underlie the AEs associated with these treatments. We review the clinical trials that influenced the regulatory history of NSAIDs, specifically COX-2 inhibitors, the role of traditional and new formulations of NSAIDs including celecoxib oral solution, and special considerations in the acute treatment of migraine attacks. Low-dose formulations of NSAIDs, such as celecoxib oral solution, provide acute migraine analgesia with similar or fewer associated cardiovascular and gastrointestinal events than previous formulations.