Problem-solving is a central competence in science education, yet its research landscape remains fragmented across domains, problem types, pedagogical contexts, outcomes, and regions. This study systematically maps global trends and thematic evolution in problem-solving research in science education from 2005 to 2025. Using a systematic literature review supported by bibliographic and multidimensional thematic mapping, 457 analysis-ready articles were selected from 10,926 initial records through a PRISMA-oriented procedure. The articles were coded according to science domain, problem type, learning context, pedagogical pathway, main outcome, research purpose, problem-solving role, geographical region, and citation indicators. The findings show substantial growth in the field, with physical science and chemistry learning dominating publication volume and outcome structures, while integrated STEM, environmental and earth science, and life and health science remain underrepresented. Structured, quantitative, diagnostic, and experimental tasks were the most established problem types, whereas open-ended, real-world, and SSI-based problems showed stronger mean citation impact despite lower frequency. Sankey and chord diagrams revealed a shift toward practical experimental contexts, authentic societal contexts, project/design pedagogy, and multidimensional outcomes. Despite these developments, authentic problems, sustainability-related contexts, interdisciplinary STEM, and project-oriented pedagogies are still frequently examined in isolation rather than as components of an integrated problem-solving framework. This review highlights the need for more integrative approaches that connect authentic problem-solving, contextual learning, sustainability, and interdisciplinary science education to support transferable competencies for addressing contemporary societal and environmental challenges.