Wireless power transfer allows the transfer of energy from a transmitter to a receiver without electrical connections. Compared to galvanic charging, it displays several advantages, including improved user experience, higher durability and better mobility. As a result, both consumer and industrial markets for wireless charging are growing rapidly. The main market share of wireless power is based on the principle of inductive power transfer, a technology based on coupled coils that transfer energy via varying magnetic fields. However, inductive charging has some disadvantages, such as high cost, heat dissipation, and bulky inductors. A promising alternative is capacitive wireless power transfer that utilizes a varying electric field as medium to transfer energy. Its wireless link consists of conductive plates. The purpose of this paper is to review the state of the art, link the theoretical concepts to practical cases and to indicate where further research is required to take next steps towards a marketable product. First, we describe the capacitive link via a coupling model. Next, we highlight the recent progress in plate topologies. Additionally, the most common compensation networks, necessary for achieving efficient power transfer, are reviewed. Finally, we discuss power electronic converter types to generate the electric field.