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Graph neural networks (GNNs) have transformed the modeling of periodic crystalline materials, enabling rapid prediction of formation energies, band gaps, elastic moduli, and interatomic forces directly from atomic coordinates. Early architectures including CGCNN and MEGNet established that message-passing on crystal graphs could rival density-functional theory (DFT) in speed while maintaining high accuracy for scalar properties. Subsequent advances introduced directional message passing (DimeNet, GemNet), equivariant architectures (E(3)-equivariant networks, MACE), graph attention mechanisms, and multi-scale approaches—each embodying distinct representational choices regarding node-edge features, symmetry handling, and information propagation. This systematic review synthesizes the literature not around incremental performance gains but around the fundamental representational trade-offs and hidden assumptions that govern model behavior in periodic systems. A taxonomy is developed organized by invariance versus equivariance, distance-only versus directional versus angular features, shallow versus deep message passing, and global pooling strategies. Four core trade-offs are analyzed: invariance against equivariance, local against global information capture, model depth against over-smoothing, and computational cost against expressivity. Beyond these, seven rarely articulated hidden assumptions are exposed—cutoff-radius sufficiency, primitive-cell representativeness, distance-only edge sufficiency, global-pooling adequacy, cubic-crystal benchmark bias, DFT-label perfection, and i.i.d. data assumptions—each critically limiting generalization to real-world materials discovery contexts. Empirical comparisons consistently favor newer architectures on standard benchmarks yet rarely isolate the contribution of individual design choices or report failure modes for low-symmetry crystals, extrapolation tasks, or long-range physics. Persistent gaps remain in long-range interaction modeling, uncertainty quantification, extrapolation capability, multi-property trade-offs, and interpretability. By reframing the crystal GNN literature through these lenses, this review offers a structured roadmap for future architecture development that prioritizes robustness and transparency over raw benchmark scores.