The article provides a comprehensive review of the flexoelectric effect in solids, emphasizing its fundamental principles, experimental studies, and potential applications. Flexoelectricity, the coupling between polarization and strain gradients, is distinct from piezoelectricity, which couples strain and electrical polarization. The review highlights the importance of strain gradients in nanoscale materials, where large strain gradients can lead to significant flexoelectric phenomena. Key topics include the phenomenological description of the flexoelectric effect, both in bulk and finite samples, microscopic calculations, and experimental methods for quantifying the flexoelectric response. The article also discusses the challenges and open questions in the field, such as the large flexoelectric coefficients observed in certain materials and the difficulty in separating bulk and surface contributions. Despite these challenges, the review underscores the potential of flexoelectricity in various applications, including piezoelectric meta-materials and strain gradient engineering.The article provides a comprehensive review of the flexoelectric effect in solids, emphasizing its fundamental principles, experimental studies, and potential applications. Flexoelectricity, the coupling between polarization and strain gradients, is distinct from piezoelectricity, which couples strain and electrical polarization. The review highlights the importance of strain gradients in nanoscale materials, where large strain gradients can lead to significant flexoelectric phenomena. Key topics include the phenomenological description of the flexoelectric effect, both in bulk and finite samples, microscopic calculations, and experimental methods for quantifying the flexoelectric response. The article also discusses the challenges and open questions in the field, such as the large flexoelectric coefficients observed in certain materials and the difficulty in separating bulk and surface contributions. Despite these challenges, the review underscores the potential of flexoelectricity in various applications, including piezoelectric meta-materials and strain gradient engineering.