Flexoelectricity is a property of all insulators that allows them to polarize under inhomogeneous deformation. Unlike piezoelectricity, which relies on symmetry-breaking in non-centrosymmetric materials, flexoelectricity arises from strain gradients in any material. While initially overlooked due to its small magnitude in bulk materials, flexoelectricity has gained renewed interest with the development of nanoscale technologies, where large strain gradients can lead to significant flexoelectric effects. This review discusses the fundamentals of flexoelectricity, its presence in nanoscale systems, and potential applications. It also highlights open questions and unresolved issues in the field. Flexoelectricity is governed by a fourth-rank tensor and is allowed in materials of any symmetry, unlike piezoelectricity, which requires non-centrosymmetric materials. The flexoelectric effect can be visualized at the microscopic level, where strain gradients cause local symmetry breaking and induce polarization. For example, in a simple ionic lattice, a vertical strain gradient can cause a central cation to shift, breaking local centrosymmetry and inducing polarity. The flexoelectric effect is a subtle physical phenomenon, and its intuitive understanding can be misleading. For instance, the sign of the flexoelectric response in a given scenario may be incorrect. The effect is not only influenced by ionic positions but also by an asymmetric redistribution of electron density, contributing to the total polarization. Flexoelectricity in graphene is controlled by this mechanism. Flexoelectricity is important because it enables additional electromechanical functionalities not available through piezoelectricity. It can act as an equivalent electric field, enabling polarization switching in ferroelectric materials. Unlike piezoelectricity, which is limited by symmetry, flexoelectricity can be used in a wide range of materials and is particularly relevant in nanoscale systems. Theoretical work on flexoelectricity dates back to the 1950s, with early contributions from Mashkevich, Tolpygo, and Kogan. The flexoelectric effect has been studied in various materials, including centrosymmetric and non-centrosymmetric systems. The static and dynamic responses of flexoelectricity have been analyzed, showing that the flexoelectric coefficient is proportional to the dielectric permittivity of the material. Experimental studies have shown that flexoelectricity can be measured using methods such as cantilever bending and pyramid compression. These methods have revealed large flexoelectric coefficients in materials like barium titanate, relaxor PMN, and (Pb, Sr)TiO3. Theoretical calculations have also been used to estimate flexoelectric coefficients, with results showing good agreement with experimental data for some materials. Despite significant experimental and theoretical efforts, reliable quantification of the flexoelectric response remains challenging. The effects of surface piezoelectricity and dynamic flexoelectricity complicate the measurement of bulk flexoeFlexoelectricity is a property of all insulators that allows them to polarize under inhomogeneous deformation. Unlike piezoelectricity, which relies on symmetry-breaking in non-centrosymmetric materials, flexoelectricity arises from strain gradients in any material. While initially overlooked due to its small magnitude in bulk materials, flexoelectricity has gained renewed interest with the development of nanoscale technologies, where large strain gradients can lead to significant flexoelectric effects. This review discusses the fundamentals of flexoelectricity, its presence in nanoscale systems, and potential applications. It also highlights open questions and unresolved issues in the field. Flexoelectricity is governed by a fourth-rank tensor and is allowed in materials of any symmetry, unlike piezoelectricity, which requires non-centrosymmetric materials. The flexoelectric effect can be visualized at the microscopic level, where strain gradients cause local symmetry breaking and induce polarization. For example, in a simple ionic lattice, a vertical strain gradient can cause a central cation to shift, breaking local centrosymmetry and inducing polarity. The flexoelectric effect is a subtle physical phenomenon, and its intuitive understanding can be misleading. For instance, the sign of the flexoelectric response in a given scenario may be incorrect. The effect is not only influenced by ionic positions but also by an asymmetric redistribution of electron density, contributing to the total polarization. Flexoelectricity in graphene is controlled by this mechanism. Flexoelectricity is important because it enables additional electromechanical functionalities not available through piezoelectricity. It can act as an equivalent electric field, enabling polarization switching in ferroelectric materials. Unlike piezoelectricity, which is limited by symmetry, flexoelectricity can be used in a wide range of materials and is particularly relevant in nanoscale systems. Theoretical work on flexoelectricity dates back to the 1950s, with early contributions from Mashkevich, Tolpygo, and Kogan. The flexoelectric effect has been studied in various materials, including centrosymmetric and non-centrosymmetric systems. The static and dynamic responses of flexoelectricity have been analyzed, showing that the flexoelectric coefficient is proportional to the dielectric permittivity of the material. Experimental studies have shown that flexoelectricity can be measured using methods such as cantilever bending and pyramid compression. These methods have revealed large flexoelectric coefficients in materials like barium titanate, relaxor PMN, and (Pb, Sr)TiO3. Theoretical calculations have also been used to estimate flexoelectric coefficients, with results showing good agreement with experimental data for some materials. Despite significant experimental and theoretical efforts, reliable quantification of the flexoelectric response remains challenging. The effects of surface piezoelectricity and dynamic flexoelectricity complicate the measurement of bulk flexoe