This chapter examines how crucial input and process characteristics of schooling are related to cognitive student outcomes. It was hypothesized that teacher quality predicts instructional quality and student achievement, and that instructional quality in turn predicts student achievement. The strengths of these relations may vary across countries, making it impossible to draw universal conclusions. However, similar relational patterns could be evident within regions of the world. These hypotheses were investigated by applying multi-level structural equation modeling to grade four student and teacher data from TIMSS 2011. The sample included 205,515 students from 47 countries nested in 10,059 classrooms. Results revealed that teacher quality was significantly related to instructional quality and student achievement, whereas student achievement was not well predicted by instructional quality. Certain characteristics were more strongly related to each other in some world regions than in others, indicating regional patterns. Participation in professional development activities and teachers' sense of preparedness were, on average, the strongest predictors of instructional quality across all countries. Professional development was of particular relevance in Europe and Western Asian/Arabian countries, whereas preparedness played an important role in instructional quality in South-East Asia and Latin America. The ISCED level of teacher education was on average the strongest predictor of student achievement across all countries; this characteristic mattered most in the Western Asia/Arabia region.