Following the requirement of the plasma processing industry for the increased throughput, the capacitively coupled plasma (CCP) reactors with large-area electrodes driven by very high-frequency sources have been proposed. However, such reactors with plasmas inside support modes which can negatively influence the uniformity of the flux or average energy of the ions impinging on the substrate, the uniformity being an essential demand of the industrial plasma processing. It is shown when the popular electrostatic approximation used for the description of the fields in CCPs breaks down and when these modes must be treated electromagnetically. Influence of the modes on the essential parameters of the CCP discharges is discussed. A few techniques for avoiding excitation of the modes leading to the undesired non-uniformities are mentioned. Results of several experiments studying such plasma discharges are briefly reviewed.