Islamic social finance has increasingly been discussed as a complementary framework for addressing poverty, inequality, financial exclusion, and development financing gaps. Yet the literature remains dispersed across studies of zakat, waqf, digital governance, institutional performance, and the Sustainable Development Goals (SDGs). This article develops a more integrative synthesis by reviewing peer-reviewed studies published mainly between 2013 and 2024 and by organizing the evidence around four linked questions: how zakat contributes to poverty alleviation, how productive waqf supports long-term development, how Islamic social finance aligns with the SDGs, and which governance factors condition institutional effectiveness. The review follows a structured PRISMA-informed process and uses thematic synthesis rather than meta-analysis because the literature contains conceptual papers, case studies, bibliometric mapping, framework-building research, and empirical analyses with heterogeneous designs. The review shows that Islamic social finance performs at least three distinct but interrelated functions. First, zakat operates as a redistributive and welfare-stabilizing instrument that can improve household resilience and reduce selected poverty indicators when targeting and institutional quality are strong. Second, productive waqf creates a longer time horizon by converting endowed assets into sustainable income streams for education, health, microenterprise, and community infrastructure. Third, integration across social and commercial Islamic finance broadens scale, sustainability, and policy relevance. At the same time, the literature consistently identifies governance weaknesses, fragmented databases, weak reporting, limited professionalism among managers, and uneven digital adoption as the main obstacles to impact. The article concludes that Islamic social finance has real developmental value, but its contribution becomes stronger when institutions move beyond charity administration toward integrated governance, data transparency, and outcome-oriented social investment.