High-entropy materials, especially high-entropy alloys and oxides, have gained significant interest over the years due to their unique structural characteristics and correlated possibilities for tailoring of functional properties. The developments in the area of high-entropy oxides are highlighted here, with emphasis placed on their fundamental understanding, including entropy-dominated phase-stabilization effects and prospective applications, e.g., in the field of electrochemical energy storage. Critical comments on the different classes of high-entropy oxides are made and the underlying principles for the observed properties are summarized. The diversity of materials design, provided by the entropy-mediated phase-stabilization concept, allows engineering of new oxide candidates for practical applications, warranting further studies in this emerging field of materials science.