The semicarbazide-sensitive amine oxidase (SSAO), also known as vascular adhesion protein-1 (VAP-1) or primary amine oxidase (PrAO), is a deaminating enzyme highly expressed in vessels that generates harmful products as a result of its enzymatic activity. As a multifunctional enzyme, it is also involved in inflammation through its ability to bind and promote the transmigration of circulating leukocytes into inflamed tissues. Inflammation is present in different systemic and cerebral diseases, including stroke and Alzheimer’s disease (AD). These pathologies show important affectations on cerebral vessels, together with increased SSAO levels. This review summarizes the main roles of SSAO/VAP-1 in human physiology and pathophysiology and discusses the mechanisms by which it can affect the onset and progression of both stroke and AD. As there is an evident interrelationship between stroke and AD, basically through the vascular system dysfunction, the possibility that SSAO/VAP-1 could be involved in the transition between these two pathologies is suggested. Hence, its inhibition is proposed to be an interesting therapeutical approach to the brain damage induced in these both cerebral pathologies.