Cities account for approximately 70% of global Carbon-Dioxide (CO₂) emissions and three-quarters of primary energy consumption, which makes urban systems the central arena for any credible pathway to net-zero greenhouse-gas output by mid-century. Achieving carbon neutrality in a smart city simultaneously requires minimising energy demand, maximising renewable penetration, electrifying transport, retrofitting the existing building stock, and preserving quality of life under heterogeneous stakeholder preferences. These objectives are mutually conflicting, high-dimensional, non-convex, and constrained by physical, financial and regulatory couplings that render classical gradient-based methods inadequate. This paper synthesises more than two decades of research on Evolutionary Multi-objective Optimization (EMO) as applied to carbon-neutral smart cities, organised around three contributions: 1) we provide a structured taxonomy of the principal EMO paradigms—domination-based (Non-dominated Sorting Genetic Algorithm II (NSGA-II), NSGA-III), decomposition-based (Multi-objective Evolutionary Algorithm based on Decomposition (MOEA/D), Reference-Vector-guided Evolutionary Algorithm (RVEA)), and indicator-based (SMS-EMOA, Hypervolume Estimation Algorithm (HypE))—together with the benchmark suites (ZDT, DTLZ, CEC 2009, MaF) and quality indicators (Hypervolume (HV), Inverted Generational Distance (IGD), ε, spacing) that have become the de-facto evaluation protocol, 2) we review four canonical application domains—building energy retrofit, microgrid planning and dispatch, multimodal transportation, and integrated district-scale urban planning—and consolidate reported carbon-reduction ranges of 30–63%, 15–45%, 12–38%, and 20–50% respectively, and 3) we critically examine the field's principal limitations: benchmark over-fitting, weak reproducibility, limited preference articulation, and the absence of standardised uncertainty quantification. We close with a five-point research roadmap—surrogate-assisted EMO, adaptive operator selection, data-driven preference learning, federated urban optimization, and reproducibility infrastructure—intended to bridge the gap between algorithmic sophistication and policy-grade deployment.