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Active distribution networks face growing renewable curtailment as distributed photovoltaic and wind generation increasingly encounter voltage, congestion, and flexibility constraints. Battery storage scheduling under uncertainty has become a central operational strategy for absorbing otherwise curtailed energy and improving distribution-level renewable integration. Despite substantial growth in optimization-based storage studies, the literature remains fragmented across stochastic programming, chance-constrained optimization, robust optimization, and distributionally robust formulations. No critical review has systematically compared these paradigms for storage scheduling and curtailment reduction specifically in active distribution networks. This critical review assesses and contrasts stochastic and robust optimization models for battery storage scheduling aimed at reducing renewable curtailment in active distribution networks. It evaluates how these approaches represent uncertainty, network constraints, operational objectives, and implementation readiness. A structured critical review of 27 peer-reviewed journal articles published between 2017 and 2024 was conducted. The analysis focuses on mathematical formulations, uncertainty modeling, storage representation, curtailment objectives, network constraints, and operational applicability. Stochastic models offer strong expected-performance reasoning but often depend on scenario quality and can become computationally demanding. Robust models provide stronger protection against adverse uncertainty realizations but may become conservative when uncertainty sets are poorly calibrated, while gaps remain in real-time scheduling, multi-service operation, degradation modeling, and field validation. The choice between stochastic and robust optimization depends on operator risk preference, data availability, computational resources, and distribution network complexity. Hybrid, data-driven, and implementation-oriented methods offer promising future pathways for reducing renewable curtailment through battery storage scheduling.

Smart-grid optimization increasingly integrates digital twins, reinforcement learning, and cyber-physical resilience analytics into a shared research space. This convergence reflects a shift from isolated grid-control studies toward data-intensive, adaptive, and resilience-oriented infrastructure analytics. This bibliometric review maps the research landscape at the intersection of these three domains. It quantifies publication trends, identifies thematic clusters, and interprets emerging fronts in smart-grid optimization research. A structured bibliometric protocol was applied to 28 peer-reviewed journal articles published between 2017 and 2025. Co-word analysis, citation analysis, thematic clustering, and citation burst interpretation were used to organize the evidence base. The analysis reveals rising publication activity after 2019 and three dominant thematic clusters. Digital twin research centers on simulation and cyber-physical representation, reinforcement learning emphasizes adaptive grid control, and cyber-resilience analytics focuses on vulnerability, disruption, and recovery. The field is moving toward integrated frameworks that combine digital twins and reinforcement learning for proactive, cyber-resilient grid optimization. These fronts suggest a growing need for real-time, explainable, and safety-aware analytics.