Neurological brain injury (NBI) remains the most feared complication following thoracic endovascular aortic repair (TEVAR), and can manifest as clinically overt stroke and/or more covert injury, detected only on explicit neuropsychological testing. Microembolic signals (MES) detected on transcranial Doppler (TCD) monitoring of the cerebral arteries during TEVAR and the high prevalence and incidence of new ischaemic infarcts on diffusion-weighted magnetic resonance imaging (DW-MRI) suggests procedure-related solid and gaseous cerebral microembolisation to be an important cause of NBI. Any intervention that can reduce the embolic burden during TEVAR may, therefore, help mitigate the risk of stroke and the covert impact of ischaemic infarcts to the function of the brain. This perspective article provides an understanding of the mechanism of stroke and reviews the available evidence regarding potential neuroprotective strategies that target high-risk procedural steps of TEVAR to reduce periprocedural cerebral embolisation.