Flexoelectricity, as a fundamental electromechanical coupling effect between electric polarization and mechanical strain gradient, or vice versa between electric polarization gradient and mechanical gradient, exists in various categories of materials including solid materials, liquid crystals, polymers, and biomembranes. Dependence of electric or mechanical gradients on geometry requires the adoption of specific structures for different flexoelectric mode applications. Scaling effect associated with gradient suggests that flexoelectric effect can be more significant in micro/nano systems, comparable to or even exceed piezoelectricity. In this review, flexoelectricity in those studied materials will be summarized and compared. Applications in sensors, actuators, capability of tuning the ferroelectric thin film properties, and roles in bio-system mechanosensitivity and mechanotranduction of flexoelectricity will be introduced respectively. Especially, flexoelectricity nano-generator enlightens a new technique for energy harvesting. Comparison with piezoelectric nano-generator suggests that flexoelectric counterpart can yield enhanced performance with specific nanostructures and provide a wider materials choice.