Objective: To review comparisons of the effectiveness of endovascular stent grafting (ESG) against open surgical repair (OSR) for treatment of chronic arch or descending thoracic aortic aneurysms (TAA). Design: Systematic review and meta-analysis Data sources: MEDLINE, EMBASE, CENTRAL, WHO International Clinical Trials Routine data collection, current controlled trials, clinical trials and the NIHR portfolio were searched from January 1994 to March 2020. Eligibility criteria for selective studies: All identified studies that compared ESG and OSR, including randomised controlled trials (RCTs), quasi-randomised and non-RCTs, comparative cohort studies and case–control studies matched on main outcomes were sought. Participants had to receive elective treatments for arch/descending (TAA). Studies were excluded where other thoracic aortic conditions (eg, rupture or dissection) were reported, unless results for patients receiving elective treatment for arch/descending TAA reported separately. Data extraction and synthesis: Data were extracted by one reviewer and checked by another. Risk of Bias was assessed using the ROBINS-I tool. Meta-analysis was conducted using random effects. Where meta-analysis not appropriate, results were reported narratively. Results: Five comparative cohort studies met inclusion criteria, reporting 3955 ESG and 21 197 OSR patients. Meta-analysis of unadjusted short-term (30 day) all-cause mortality favoured ESG (OR 0.75; 95% CI 0.55 to 1.03)). Heterogeneity identified between larger and smaller studies. Sensitivity analysis of four studies including only descending TAA showed no statistical significance (OR 0.73, 95% CI 0.45 to 1.18)), moderate heterogeneity. Meta-analysis of adjusted short-term all-cause mortality favoured ESG (OR 0.71, 95% CI 0.51 to 0.98)), no heterogeneity. Longer-term (beyond 30 days) survival from all-cause mortality favoured OSR in larger studies and ESG in smaller studies. Freedom from reintervention in the longer-term favoured OSR. Studies reporting short-term non-fatal complications suggest fewer events following ESG. Conclusions: There is limited and increasingly dated evidence on the comparison of ESG and OSR for treatment of arch/descending TAA. PROSPERO registration number: CRD42017054565.