Visceral artery aneurysms (VAAs) are rare and affect the celiac artery, superior mesenteric artery, and inferior mesenteric artery, and their branches. The natural history of VAAs is not well understood as they are often asymptomatic and found incidentally; however, they carry a risk of rupture that can result in death from hemorrhage in the peritoneal cavity, retroperitoneal space, or gastrointestinal tract. Recent advances in imaging technology and its availability allow us to diagnose all types of VAA. VAAs can be treated by open surgery, laparoscopic surgery, endovascular therapy, or a hybrid approach. However, there are still no specific indications for the treatment of VAAs, and the best strategy depends on the anatomical location of the aneurysm as well as the clinical presentation of the patient. This article reviews the literature on the etiology, clinical features, diagnosis, and anatomic characteristics of each type of VAA and discusses the current options for their treatment and management.