Several computational tools have been developed to detect and identify sexism, misogyny, and gender-based hate speech, particularly on online platforms. These tools draw on insights from both social science and computer science. Given the increasing concern over gender-based discrimination in digital spaces, the contested definitions and measurements of sexism, and the rise of interdisciplinary efforts to understand its online manifestations, a systematic literature review is essential for capturing the current state and trajectory of this evolving field. In this review, we make four key contributions: (1) we synthesize the literature into five core themes: definitions of sexism and misogyny, disciplinary divergences, automated detection methods, associated challenges, and design-based interventions; (2) we adopt an interdisciplinary lens, bridging theoretical and methodological divides across disciplines; (3) we highlight critical gaps, including the need for intersectional approaches, the under-representation of non-Western languages and perspectives, and the limited focus on proactive design strategies beyond text classification; and (4) we offer a methodological contribution by applying a rigorous semi-automated systematic review process guided by PRISMA, establishing a replicable standard for future work in this domain. Our findings reveal a clear disciplinary divide in how sexism and misogyny are conceptualized and measured. Through an evidence-based synthesis, we examine how existing studies have attempted to bridge this gap through interdisciplinary collaboration. Drawing on both social science theories and computational modeling practices, we assess the strengths and limitations of current methodologies. Finally, we outline key challenges and future directions for advancing research on the detection and mitigation of online sexism and misogyny.