This monograph is intended to provide an overview on the achievements in the field of flexoelectricity. Flexoelectricity is a fundamental property of condensed matter, with significant potential for further scientific study, and is highly promising to many applied activities.Organized by the type of condensed matter considered -- solid, soft and living -- for detailed comparison and analysis, the focus is on the fundamentals of the topic, on experimental methods applied over the years to determine flexoelectric coefficients, as well as on reviewing different and even controversial approaches, all of which could provoke an examination of the subject with fresh eyes.