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This paper explores various methods that have been proposed for the segmentation of the cerebrovascular structure. All of the methods listed are a combination old, new, automatic and semiautomatic models that produce promising results. Each method will be explained along with its advantages and disadvantages. Each of the methods explained are further explored in this paper with variety algorithms produced by using certain models to target certain areas in the cerebrovascular structure. These algorithms were developed to segment cerebrovascular structures from scans obtained from various image modalities e.g., time of flight magnetic-resonance angiography (TOF-MRA), and computed tomography angiography (CTA).