Silicon-carbon composite materials and compounds combine the high lithium storage performances of silicon with the structural excellence of carbon. However, their complex electrochemical behavior and volume changes during charging and discharging are urgent issues to be addressed. As an effective theoretical tool, first-principles calculation plays a crucial role in predicting, revealing the characteristics of electrode materials and understanding electrochemical mechanisms in atomic scale. In this review, the first-principles calculation methods were summarized, and recent research results on first-principles calculations of typical silicon-carbon composite materials and compounds as lithium-ion battery anode materials were represented. The laws of diffusion kinetics, interface reactions, mechanical properties and thermodynamic stabilities of silicon-carbon anode materials for lithium-ion batteries were proposed. Furthermore, the first-principles calculations for silicon-carbon anode materials in lithium-ion batteries were outlooked based on three perspectives like density functional theory (DFT), algorithm integration and experimental integration. The development of novel silicon-carbon anode materials with superior performances were anticipated, thereby contributing to the development of the new energy sector.Summary and prospectsIn this review, the first-principles calculation methods and the research progress of the first-principles calculations on typical silicon-carbon anode materials for lithium-ion batteries were elaborated. The diffusion kinetics, interfacial reactions, mechanical properties and thermodynamic stability laws of silicon-carbon anode materials for lithium-ion batteries were revealed.1) From the perspective of lithium-ion diffusion kinetics, the diffusion mechanism of lithium ions in silicon-carbon anode materials is complex, which is affected by material structure and chemical composition. In silicon/graphite composite materials, lithium ions are prone to first intercalating between graphite layers and then diffusing into silicon, which is regarded as a two-dimensional diffusion. Lithium ions in silicon/carbon nanotube composite materials undergo an one-dimensional diffusion, primarily along the walls or gaps between carbon nanotubes. The two-dimensional structure in silicon/graphene composite materials facilitates a rapid diffusion of lithium ions. Lithium ions in silicon carbide exhibit bulk and interfacial diffusion, which are influenced by charge transfer and electric field effects.2) From the perspective of interface reaction, the formation of the SEI film is crucial for the performance of silicon-carbon anode materials. Meanwhile, cycle life and efficiency of the batteries are affected by stability and uniformity of SEI film. The volume expansion of silicon in silicon/graphite composite materials can damage the adjacent SEI film, leading to the continued generation of new SEI film. In silicon/carbon nanotube composite materials, more active sites for lithium ions are provided for the unique tubular structure and high specific surface area of carbon nanotubes, making the SEI film more stable. Silicon/graphene composite materials have a layered structure that promotes the uniform dispersion of electrolyte on the surface for the composite materials, resulting in a more uniform SEI film. Silicon carbide has a great hardness and a wear resistance, which enhances its ability to resist mechanical stress during charging and discharging, effectively protecting the SEI film.3) From the perspective of mechanical properties, different types of carbon materials have different buffering effects on the volume expansion of silicon. Volume expansion problems of silicon are alleviated because of impurities and defect structure of microcrystalline graphite in silicon/graphite composite materials. In silicon/carbon nanotube composite materials, the flexibility of carbon nanotubes helps to withstand greater structural deformation and enhance the structural stability of silicon. In silicon/graphene composite materials, core-shell structures are more conducive to suppressing the volume expansion of silicon. The decrease in electrochemical performance caused by volume expansion is alleviated by the tight interface bonding between silicon carbide and the matrix material, which also helps to improve the fatigue resistance of materials.4) From the perspective of thermodynamic stability, the thermodynamic stability is assessed through calculations of formation energy, binding energy, reactivity, and changes in free energy. Silicon/graphite composites, benefiting from the layered structure of graphite, exhibit a good thermodynamic stability due to their low formation energy, high binding energy, and low reactivity. Silicon/carbon nanotube composites have a high binding energy due to their unique structure, but their thermodynamic stability is significantly affected by free energy under high-temperature and high-pressure conditions. Silicon/graphene composite materials, leveraging the two-dimensional structure of graphene, have a moderate formation energy and a high binding energy, resulting in a stable thermodynamic performance. Silicon carbide has a high formation energy, and the covalent bonds between silicon and carbon atoms contribute to its high structural stability and good thermodynamic stability.Conventional DFT method struggles to accurately simulate intermolecular forces due to its lack of description of nonlocal electron correlations, resulting in significant errors in calculating material structural parameters, mechanical properties and energetic properties. To overcome this problem, the van der Waals Density Functional method is introduced. The Becke 86 exchange functional is incorporated by a named optB86b method, enabling effective corrections to the Generalized Gradient Approximation. The excessively strong repulsive interaction of the exchange functional at short distances is reduced, and the accuracy of DFT method is enhanced.To enhance the computational efficiency of first-principles calculations and have deeper insights into the lithium storage mechanism of silicon-carbon anode materials in lithium-ion batteries, the first-principles calculations and machine learning, phase-field methods, multiscale simulation techniques are integrated. The data analysis and model optimization are accelerated via machine learning. The evolution of microstructures is captured cross phase-field methods. The macroscopic reaction mechanisms of lithium-ion batteries from a microscopic perspective are revealed based on molecular dynamics and finite element analysis. The precision and efficiency of material development are significantly improved via interdisciplinary integration, expanding the application of silicon-carbon anode materials in the field of new energy.The first-principles calculations and experimental research should be combined due to some factors such as high experimental costs, stringent experimental condition and low data reproducibility. The accuracy of first-principles calculation methods can be validated via comparing computational predictions with experimental results, promoting the coordinated development of theoretical calculations and experimental research. It is expected that this will lead to the development of new silicon-carbon anode materials with a higher specific capacity, a better cycle stability, and a faster charge/discharge rate, facilitating their application in sodium-ion batteries and other fields and bringing greater breakthroughs to the development of the new energy field.