Some alien species cause substantial impacts, yet most are innocuous. Given limited resources, forecasting risks from alien species will help prioritise management. Given that risk assessment (RA) approaches vary widely, a synthesis is timely to highlight best practices. We reviewed quantitative and scoring RAs, integrating > 300 publications into arguably the most rigorous quantitative RA framework currently existing, and mapping each study onto our framework, which combines Transport, Establishment, Abundance, Spread and Impact (TEASI). Quantitative models generally measured single risk components (78% of studies), often focusing on Establishment alone (79%). Although dominant in academia, quantitative RAs are underused in policy, and should be made more accessible. Accommodating heterogeneous limited data, combining across risk components, and developing generalised RAs across species, space and time without requiring new models for each species may increase attractiveness for policy applications. Comparatively, scoring approaches covered more risk components (50% examined > 3 components), with Impact being the most common component (87%), and have been widely applied in policy (> 57%), but primarily employed expert opinion. Our framework provides guidance for questions asked, combining scores and other improvements. Our risk framework need not be completely parameterised to be informative, but instead identifies opportunities for improvement in alien species RA.