Rarefied gas dynamics addresses multiscale non-equilibrium transport problems spanning from the molecular mean free path to the continuum flow limit, and its theoretical modelling and numerical methodologies have long been important research topics in the interdisciplinary domain of fluid mechanics and statistical physics. This paper systematically reviews recent key advances in simplified solutions of the Boltzmann equation and the modeling of gas-solid boundary conditions. From the perspective of computational methods, multiscale modeling strategies, encompassing macroscopic, mesoscopic, particle-based, and hybrid methods, are summarized. At the macroscopic level, the Navier-Stokes/Burnett equations derived from the Chapman-Enskog expansion, Grad's moment method with R13 regularization, together with generalized hydrodynamics and nonlinear coupled constitutive relations, constitute the primary theoretical frameworks for correcting the continuum description beyond its regime of validity. At the particle level, the direct simulation Monte Carlo (DSMC) method, together with its information-preservation variants, and stochastic particle methods based on model kinetic equations, are widely employed numerical tools in the transitional flow regime. At the mesoscopic level, the discrete velocity method (DVM), the unified gas-kinetic scheme (UGKS) and its discrete variant (DUGKS), the unified gas-kinetic wave-particle method/unified gas-kinetic wave-particle method (UGKP/UGKWP) and simplified wave–particle coupling approaches, aim to strike a balance between computational efficiency and numerical accuracy. In addition, kinetic flux solvers and constitutive-law hybrid correction methods (e.g., DiNS and GSIS) provide complementary pathways bridging kinetic and macroscopic simulations. In this paper, emphasis is placed on elucidating the intrinsic connections and essential distinctions among the aforementioned methods in terms of their modelling rationale and numerical implementation. With regard to boundary conditions, the progressive transition of gas-solid interaction modeling from molecular descriptions to continuum representations is systematically reviewed, covering microscopic scattering kernel models (Maxwell model, CLL model and their extensions) and macroscopic velocity-slip boundary conditions (first-order linear M-S models, nonlinear slip models, and higher-order slip models). On this basis, the key challenge in current rarefied gas dynamics research is identified as establishing simplified modelling theories based on the Boltzmann equation that reconcile predictive fidelity with computational affordability, along with their compatible boundary conditions. This review aims to serve as a reference for theoretical investigations in rarefied gas dynamics and for aerospace engineering applications such as very-low-Earth-orbit satellites and deep-space exploration, while also providing a foundational framework for future methodological innovations.