Hybrid Renewable Energy Systems are pivotal for the sustainable energy transition, yet their design and operation present complex optimization challenges due to diverse components, stochastic resources, and multifaceted objectives. This systematic review formalizes the HRES optimization problem space and identifies critical research gaps. Employing the PRISMA 2020 guidelines, it comprehensively analyzes the literature (2015–2025) from Scopus, IEEE Xplore, and Web of Science, focusing on architectures, mathematical formulations, objectives, and solution methodologies. The results reveal a decisive shift from single-objective to multi-objective optimization (MOO), increasingly incorporating environmental and emerging social criteria alongside traditional economic and technical goals. Metaheuristic algorithms (e.g., NSGA-II, MOPSO) and AI techniques dominate solution strategies, though challenges persist in scalability, uncertainty management, and real-time control. The integration of hydrogen storage, vehicle-to-grid (V2G) technology, and multi-vector energy systems expands system boundaries. Key gaps include the lack of holistic frameworks co-optimizing techno-economic, environmental, social, and resilience objectives; disconnect between long-term planning and short-term operation; computational limitations for large-scale or real-time applications; explainability of AI-based controllers; high-fidelity degradation modeling for emerging technologies; and bridging the “valley of death” between simulation and bankable deployment. Future research must prioritize interdisciplinary collaboration, standardized social/resilience metrics, scalable and trustworthy AI, and validation frameworks to unlock HRESs’ potential.