Isolation of the left brachiocephalic artery (ILBA) is an extremely rare anomaly of aortic arch with diverse manifestations in the neurologic system, heart, and left upper arm. This anomaly is defined as the absence of connection of the left brachiocephalic artery (LBA) to aortic arch and connection of LBA to pulmonary artery (PA) through a patent arterial duct (PAD). However, this definition is not inclusive of all cases. Not only are there inconsistencies in the definition and terminology of this aortic arch anomaly but also there is no classification for this anomaly despite its heterogeneous nature in terms of anatomy, clinical presentation and prognosis. We performed a 52-year comprehensive literature review in the period between 1966 and 2018. Our inclusion criteria were any manuscript that included a case report or case series, with confirmed diagnosis of ILBA. All quantitative data were analyzed using descriptive analysis by SPSS version 21 (IBM SPSS Statistics, USA). Results were presented as mean ± standard deviation and median. Based on the presence or absence of connection of LBA to PA and the number of sources of steal from the LBA, we classified ILBA into three types: single-steal type with no connection of LBA to PA and single source of blood flow steal from LBA through the left subclavian artery (LSCA), double-steal type with connection of LBA to PA through PAD and two sources of steal through LSCA and arterial duct (AD), and triple-steal type with bilateral PADs and therefore, three sources of blood flow steal from LBA including the LSCA and the double ADs. Patients with single-steal type have the best prognosis and present latest with symptoms of cerebrovascular insufficiency or left arm claudication. The oldest reported patient was 69 years of age with symptoms of dizziness and near syncope. No death was reported in these patients. Double-steal type is the most common type and is often associated with genetic syndromes and/or extracardiac anomalies. Triple-steal type is the rarest type with the earliest presentation and worst prognosis. The oldest reported patient was 60 days of age. All reported cases had cardiac symptoms, pulmonary overcirculation, pulmonary hypertension, and fatal outcome.