Flexoelectricity in dielectrics suggests promising smart structures for sensors, actuators and transducers. In this review, dielectric materials, structures and the associated flexoelectric characterization methods are presented. First of all, we review structures and methods to measure different flexoelectric coefficients, including [Formula: see text], etc., via direct or converse flexoelectric effect. The flexoelectric materials in the form of bulk, thin films and 2D materials and the reported flexoelectric properties of these dielectrics will then be discussed. Semiconductor materials and the associated flexoelectric studies will also be reviewed. The progress of flexoelectric device study will next be presented, followed by the flexoelectricity research challenges and future trend.