Moyamoya angiopathy is characterized by a progressive stenosis of the terminal portion of the internal carotid arteries and the development of a network of abnormal collateral vessels. This chronic cerebral angiopathy is observed in children and adults. It mainly leads to brain ischemic events in children, and to ischemic and hemorrhagic events in adults. This is a rare condition, with a marked prevalence gradient between Asian countries and Western countries. Two main nosological entities are identified. On the one hand, moyamoya disease corresponds to isolated moyamoya angiopathy, defined as being “idiopathic” according to the Guidelines of the Research Committee on the Pathology and Treatment of Spontaneous Occlusion of the Circle of Willis. This entity is probably multifactorial and polygenic in most patients. On the other hand, moyamoya syndrome is a moyamoya angiopathy associated with an underlying condition and forms a very heterogeneous group with various clinical presentations, various modes of inheritance, and a variable penetrance of the cerebrovascular phenotype. Diagnostic and evaluation techniques rely on magnetic resonance imaging (MRI), magnetic resonance angiography (MRA) conventional angiography, and cerebral hemodynamics measurements. Revascularization surgery can be indicated, with several techniques. Characteristics of genetic moyamoya syndromes are presented, with a focus on recently reported mutations in BRCC3/MTCP1 and GUCY1A3 genes. Identification of the genes involved in moyamoya disease and several monogenic moyamoya syndromes unraveled different pathways involved in the development of this angiopathy. Studying genes and pathways involved in monogenic moyamoya syndromes may help to give insights into pathophysiological models and discover potential candidates for medical treatment strategies.