The purpose of this work is to review the computational models of the adaptive behavior of the cerebral vascular wall aimed at simulating aneurysm formation and enlargement. Cerebral aneurysms are localized abnormal enlargements of the intracranial arterial vessels. The origin of this pathology is still unclear: however, aneurysm formation is thought to be the result of interplay between biomechanical properties of the vessel wall and their possible changes, such as adaptive response to mechanical stimuli. Recently, different computational approaches were suggested in the literature aiming to describe the mechanobiology of the cerebral vascular wall. Most of the computational adaptive models showed a common approach for the geometrically non-linear kinematic description of the phenomenon, whilst the constitutive laws defining the rates of growth variables may differ considerably according to the specific phenomenon considered. These studies allowed the reproduction of some peculiar aspects of aneurysm mechanobiology; however, continued interdisciplinary research is mandatory for a better understanding of the mechanisms involved in the evolution of cerebral aneurysms.