Generative models for crystalline materials have emerged as a transformative paradigm in computational materials science, offering new possibilities for crystal structure prediction (CSP), inverse structural design, and functional materials discovery. Compared with traditional search-based CSP frameworks that depend on iterative global optimization and handcrafted physical constraints, generative approaches learn the statistical distribution of atomic arrangements directly from data, thereby enabling efficient sampling of chemically valid and symmetry-consistent structures. Recent advances in geometric deep learning, equivariant neural networks, variational autoencoders, and diffusion-based modeling have substantially enhanced both the fidelity and scalability of generative crystal models. However, despite the rapid development, a comprehensive and systematic review that integrates representations, generative mechanisms, and practical applications of these models is still sparse.

This review first analyzes the major classes of crystal representations. According to the level of geometric completeness and symmetry preservation, representations can be categorized into reciprocal-space encodings (e.g., diffraction-based descriptors), symmetry-aware Wyckoff-position formalisms, voxelized three-dimensional grids, point-cloud coordinate systems, and graph-based multirelational structures. The specific characteristics of each representation are summarized, including their capabilities for handling periodicity, long-range interactions, spatial boundary conditions, and compatibility with equivariant neural networks. Hybrid schemes—such as the point-cloud/graph combined formulations used in DiffCSP, MatterGen, and GNOME—provide balanced expressiveness and geometric accuracy, enabling efficient modeling of complex crystalline systems.

The generative mechanisms of crystal models are more intricate than those of molecular generative models. According to their learning paradigm, recent models may be divided into four categories. Multimodal-aligned models (e.g., Chemeleon) employ contrastive learning to align textual descriptions with crystal structures, enabling text-conditioned generation across complex chemical spaces. Experiment-driven models (e.g., XtalNet) directly map PXRD spectra to crystal structures via integrated pretraining and conditional generation, circumventing traditional database matching. Twin-model collaborative frameworks (e.g., DAO) combine generative modules with high-precision property predictors, achieving concurrent optimization of structural stability and targeted properties. Dynamics-informed models incorporate nonlinear kinetic effects such as impurity-induced frustration and non-equilibrium crystallization into sampling strategies. These mechanisms collectively provide diverse pathways for addressing the unique challenges posed by crystalline systems.

The applications of generative crystal models are further examined across pharmaceuticals, quantum materials, and energy-related functional materials. In pharmaceutical solid-state chemistry, pocket-conditioned molecular generative models provide insights into integrating solid-form considerations with molecular design. In quantum materials research, constraint-embedded generators such as SCIGEN enable large-scale exploration of lattice-specific structures—including Archimedean and Lieb lattices—yielding candidates for quantum spin liquids, flat-band materials, and exotic magnetic phases. In energy materials, the DAO framework demonstrates the potential of "generation-prediction" coupling by successfully designing superconductors and high-capacity layered cathodes, showing strong coherence between computational predictions and experimental verification.