The plasma environment significantly affects the atomic structures and parameters of embedded atoms, and accurately describing plasma screening effects is essential for understanding the state and evolution of matter in astrophysical objects and laboratory high-energy-density physics facilities. Owing to their intuitive physical interpretations and moderate computational cost, plasma screening models based on the single-atom approximation are widely employed in plasma diagnostic analysis and numerical simulations. This review systematically surveys the full spectrum of single-atom-based plasma screening models and their implementations in atomic structure computations. The degeneracy parameter Θ and the coupling parameter Γ_ee are adopted as a unified classification benchmark. The review is organized along two distinct developmental chains based on these parameters. The first chain originates from the Thomas-Fermi (TF) formalism, encompassing the classical Debye-Hückel (DH) model, the non-extensive modified DH model that accounts for statistical fluctuations, the cosine-screened Coulomb potential, which incorporates quantum diffraction effects, and the gradient-corrected screening model that includes gradient corrections and exchange-correlation effects within the framework of orbital-free density functional theory. This chain traces the theoretical improvements extending from ideal or weakly coupled plasmas to warm dense matter regimes. The second chain starts from the ion-sphere ansatz, evolving from the uniform-electron-density ion-sphere model, self-consistent ion-sphere models that determines the spatial distribution of the electron density self-consistently, the analytical ion-sphere model, to the two-step Hartree-Fock-Slater model, and the valence-band bound-free-continuum screening model. This chain demonstrates progressive refinements in describing electron non-uniformity and band formation in strongly coupled plasmas. On this theoretical basis, we elaborate two models developed by our group alongside their applications in atomic structure calculations. (1) the partitioned DH model, which corrects the short-range deficiency of the standard DH model through a spatial partitioning strategy. Scaling laws are established for transition-energy shifts and oscillator strengths as functions of the plasma screening intensity across multiple isoelectronic sequences ranging from H-like to C-like ions. (2) the atomic-state-dependent plasma screening model, which incorporates the contribution of band electrons and the influence of inelastic scattering processes on the electron distribution. This model provides a unified screening framework that can be applied in a wide range of plasma parameters, ranging from weakly to strongly coupled regimes and from non-degenerate to strongly degenerate conditions. This review intends to provide the reader a coherent and holistic overview of single-atom-approximation-based plasma screening models. We want to elucidate the intrinsic connections and evolutionary relationships among different models, and present their current applications in atomic structure and parameter calculations. We hope this review can deliver practical guidance for selecting appropriate screening models in plasma atomic structure computations.