In the present meta-analysis, we examine how secondary school characteristics -- such as schools' academic press, school climate, material resources, personnel resources, classroom climate, instructional practices, out-of-school activities, and socioeconomic status (SES) composition -- provide opportunities for students to engage in science and maths, and how these matter with regard to students' cognitive and motivational-affective outcomes. The meta-analysis includes 71 (international) articles from large-scale studies with a total of 3,960,281 students, 260,390 schools, and 285 effect sizes that were transformed to correlation coefficients. Multilevel meta-analyses were performed. Results identified a number of school variables that can be regarded as relevant for making a difference in student outcomes and at the same time be influenced by education. These refer to school variables such schools' academic press, classroom climate, instructional practices, and out-of-school activities. Moreover, SES composition was significantly related to student outcomes. Material and personnel resources as well as school climate yielded a close to zero effect. No differences were found between cognitive and motivational-affective outcome variables or between science and maths. The results point to the most promising school characteristics for promoting students' outcomes and emphasise schools' potential for students' engagement in science and maths.