Energy saving and carbon reduction in pumping systems at urban water supply plants are pivotal for achieving carbon-peak and carbon-neutrality goals. Over 90% of the electricity consumption in such plants is attributed to pump operation. However, current research faces three interconnected problems. First, static models based on theoretical characteristics fail to represent actual dynamic operating conditions accurately, leading to biased optimization baselines. Second, the coupling between intelligent algorithms and increasingly complex pump-optimization problems remains insufficient, often resulting in suboptimal solutions. Third, the evaluation system is fragmented, and assessment results are not effectively fed back into the optimization process to enable iterative improvement. These disconnections among the Model–Algorithm–Assessment components represent a core scientific challenge that hinders precise and effective decarbonization of water-supply systems. This review systematically examines recent advances in the application of intelligent algorithms to pump-energy optimization. It first outlines the key elements of pump-energy modeling, including operating-point derivation via curve fitting, objective-function formulation, and constraint setting, which together provide a foundation for subsequent algorithmic optimization. It then categorizes and analyzes application scenarios and technical features of traditional heuristics, data-driven methods, and hybrid algorithms. Literature analysis shows that traditional heuristics remain the most widely applied but are prone to premature convergence under dynamic conditions, limiting their practical effectiveness. In contrast, emerging hybrid algorithms that integrate mechanistic models with data-driven techniques have demonstrated additional energy-saving potential: specifically, they can reduce energy consumption by 5%–10% compared to traditional algorithms. A life-cycle perspective indicates that operational-phase carbon emissions account for 70%–85% of the total footprint, while manufacturing and disposal stages contribute 15%–30%. This finding suggests that life-cycle assessment (LCA) could complement existing evaluation systems and underscores the need for a holistic assessment beyond mere operational energy use. Operational-phase metrics are also detailed, as they are essential for quantifying optimization effects and providing feedback to algorithms. The results indicate that the iterative synergy between intelligent algorithms and assessment systems is central to enhancing performance. To address the identified gaps, we propose a Model–Algorithm–Assessment trinity framework that focuses on three interrelated aspects: (1) a sufficiently accurate and generalizable mathematical model; (2) intelligent algorithms that overcome algorithm–problem mismatch and achieve efficient optimization under complex, time-varying conditions; and (3) a life-cycle assessment system that provides comprehensive validation and broader evaluation dimensions for optimization strategies. This framework promotes the implementation of intelligent energy-saving and carbon-reduction technologies in urban water-supply plants.