<p>This article presents a systematic review of research on the teaching and learning of quadratic equations. A configurative approach to qualitatively synthesize research was employed, searching four databases: Scopus, Web of Science, PsycInfo, and ERIC. A total of 38 papers (26 journal articles and 12 conference papers) with empirical findings from mostly secondary school students, ages 13–17, across multiple countries, were included. Findings from research on teaching show that geometry-aided approaches, specific to quadratic equations for factoring and completing the square, show promise for promoting understanding and interest. Forms of instruction being general or using technology also indicate positive findings; however, evidence remains limited. Studies on learning identified several issues corresponding to concepts and methods for solving quadratic equations, many due to lacking pre-requisite knowledge. These were framed as lacking flexibility, having non-relational types of understandings, or being due to student properties and instructional context. Proposed implications from research for teaching showed specific instruction to be included, that teaching should focus on conceptual understanding, that planning instruction should be informed by student thinking, and that curriculum could be adjusted for long-term coherence. Combining these findings, mastering quadratic equations requires developing flexible knowledge by connecting multiple solution strategies with conceptual understanding, supported by teaching that links concepts to procedures through varied examples, formative assessment, and visual or technological aids. The implications of this review for practice include informing teaching and development of instructional resources while considering local context. Future research should examine effects of instructional approaches targeting specific aspects of quadratic equations.</p>