Devices for the endovascular embolization of intracranial aneurysms (ICAs) face limitations related to suboptimal rates of lasting complete occlusion. Incomplete occlusion frequently leads to residual flow within the aneurysm sac, which subsequently causes aneurysm recurrence needing surgical re-operation. An emerging method for improving the rates of complete occlusion both immediately after implant and in the longer run can be the fabrication of patient-specific materials for ICA embolization. Shape memory polymers (SMPs) are materials with great potential for this application, owing to their versatile and tunable shape memory properties that can be tailored to a patient’s aneurysm geometry and flow condition. In this review, we first present the state-of-the-art endovascular devices and their limitations in providing long-term complete occlusion. Then, we present methods for the fabrication of SMPs, the most prominent actuation methods for their shape recovery, and the potential of SMPs as endovascular devices for ICA embolization. Although SMPs are a promising alternative for the patient-specific treatment of ICAs, there are still limitations that need to be addressed for their application as an effective coil-free endovascular therapy.