Accurate plant-scale wake modeling is essential for wind-farm design, control, and digital-twin operation, yet practical prediction remains constrained by the fidelity–deployability trade-off between fast engineering wake models and physics-rich computational fluid dynamics (CFD). Machine learning (ML) has expanded rapidly as a route to low-latency wake prediction and multi-fidelity correction, but existing studies remain difficult to compare because they differ in learned outputs, data provenance, and validation claims. This review reframes ML wake modeling around the predicted physical quantity rather than the algorithm alone. Four task families are distinguished: scalar response or key performance indicator (KPI) prediction, static wake-field or wake-state emulation, dynamic wake evolution, and turbine–turbine interaction-operator learning. For each family, we examine how representative architectures, including tabular surrogates, convolutional and recurrent models, graph neural networks, neural operators, reduced-order models, and physics-informed learning, embed inductive biases for spatial locality, temporal memory, directional coupling, coherent wake structure, and discretization-aware mapping. We further synthesize data regimes spanning engineering models, CFD, aero-servo-elastic simulation, supervisory control and data acquisition (SCADA), light detection and ranging (LiDAR), and wind-tunnel measurements, emphasizing how label fidelity, sample independence, operational confounding, and solver-specific assumptions shape the sim-to-real gap. Building on this taxonomy, we propose claim-driven benchmarking that aligns hold-out design, physics-aware diagnostics, uncertainty calibration, and deployment evidence across regime, layout, control-policy, site, discretization, and fidelity shifts. The review identifies where current ML wake models are mature, where validation remains weak, and how future work can support robust layout optimization, wake steering, load-aware control, and wind-farm digital twins.