This work explores the phenomenon of flexoelectricity in nanomaterials and nanostructures by molecular dynamics models and continuum models. Flexoelectricity is an electromechanical phenomenon describing the coupling between electric polarization and strain gradient in a material. Thanks to the strain gradient term, flexoelectricity exhibits an universal existence and size-dependent behavior, enabling strong electromechanical coupling at micro/nanoscale, leading to ideal application in micro/nano-devices, such as Nanogenerator. However, it is difficult to measure or estimate the intrinsic flexoelectric coefficients of a material due to the interference from the piezoelectric effect, representing the coupling between electric polarization and strain. Additionally, the standard continuum model, such as the finite element model, cannot accommodate flexoelectricity due to the higher-order continuity requirement(C1 continuity) imposed by the strain gradient term, requiring the development of novel continuum approaches for the design guidance of flexoelectric devices. These difficulties limit our understanding and potential engineering utilization of flexoelectricity.In the framework of molecular dynamics, this work develops a core-shell and charge-dipole model for extracting flexoelectric coefficients of a traditional electromechanical material (BaTiO3) and newly emerged two-dimensional (2D) materials (in total 21 materials), respectively. Specially designed mechanical loading schemes are employed within the core-shell and charge-dipole model to eliminate the interference from piezoelectricity, enabling direct measurement of the materials’ flexoelectric response. The core-shell models’ results show that the size/surface effect significantly influences the longitudinal and shear flexoelectric coefficient of the BaTiO3 nanostructures. For two-dimensional materials, the charge-dipole model extracted their bending flexoelectric coefficients and identified their contributors. It observes that transition metal dichalcogenide monolayers possess the highest flexoelectric coefficients among the studied 2D materials.This work also develops continuum models to characterize flexoelectricity in continuumsolid structures, such as flexoelectric composite. A 2D Meshless model and a 3D nonlinear mixed finite element model employ higher-order shape function and extra degrees of freedom to fulfill the C1 continuity requirement of flexoelectricity. Both models show that structure configurations and material properties influence the electromechanical behavior of flexoelectric composites. Besides, the 3D nonlinear mixed finite element model demonstrated the essentialness of the geometrical nonlinearity for an accurate representation of flexoelectricity by continuum models.