This literature review analyzes the latest modeling frameworks for composite structures and functionally gradient materials, emphasizing Equivalent Single-Layer (ESL) theories, layer-by-layer formulations (layerwise) and the Carrera Unified Formulation (CUF) as well as their applications to beams, plates, sandwich structures, and materials with functional gradients (FGM). Our aim is to clarify the modeling trade-offs that determine the theory choice based on the structure's thinness, heterogeneity through thickness, and complexity of multilayer stacks. ESL approaches, ranging from classical theory to first- and higher-order shear models, are distinguished by their low computational cost and ability to conduct large-scale analyses, but often require enriched kinematics or specific corrections to ensure sufficient accuracy in the case of thick structures, marked gradients, or interlaminar effects. Layerwise models, which include discrete and mixed formulations, offer a more precise description of fields across thickness and interfaces, but come with an increased number of degrees of freedom enabling them to analyze sandwich and FGM structures that are susceptible to delamination. The CUF is analyzed as a unifying framework that allows for systematic priority of kinematics and controlled adjustment of the trade-off between accuracy and cost, with a goal of convergence towards predictions close to three-dimensional elasticity. Based on the identified works, a comparative synthesis is proposed in terms of accuracy, numerical robustness, and computational cost for the analysis of flexure, vibration, and buckling, as well as for some nonlinear and multiphysical extensions.