Low-dose aspirin remains the most commonly used antiplatelet agent among patients with atherosclerotic cardiovascular disease. Aspirin hypersensitivity occurs in 1% to 5% of patients and is among the most frequent causes for prohibiting the use of aspirin, posing a significant dilemma on how to manage these patients in clinical practice. Aspirin hypersensitivity is often misinterpreted and confused with aspirin intolerance, with treatment approaches being often unclear and lacking specific recommendations. Aspirin desensitization and low-dose aspirin challenge have emerged as pragmatic, effective, and safe approaches in patients with suspected or confirmed aspirin hypersensitivity who require aspirin therapy, but they are underused systematically in clinical practice. Furthermore, there is confusion over alternative antiplatelet agents to be used in these patients. The pathophysiological mechanisms and classification of aspirin hypersensitivity, as well as alternative strategies and practical algorithms to overcome the need for aspirin use in patients with atherosclerotic cardiovascular disease with suspected aspirin hypersensitivity, are discussed.