For the last 50 years, social, educational, and behavioral scientists investigating the relationships among school socioeconomic (SES) composition and educational outcomes have demonstrated time and again that schools with higher concentrations of students living in poverty provide less than optimal teaching and learning conditions, and they are especially harmful to the most vulnerable students who are, most often, youth living in neighborhoods of concentrated poverty and low-income students of color. Concentrated poverty in schools creates and sustains disparities in academic outcomes. High concentrations of students living in poverty complicate learning and teaching in schools, and reduce the effectiveness of other educational interventions designed to address gaps in academic outcomes. Short-term, "band-aid" solutions may improve some outcomes for some students in a particular school in a given year, but any gains are not sustained in the long-term. This research brief summarizes recent research about school SES composition effects on educational outcomes, with a focus on whether this enormous cross-disciplinary body of research supports claims that school poverty "thresholds" or "tipping points" exist.