A radome is an integral part of almost every antenna system, protecting antennas and antenna electronics from hostile exterior conditions (humidity, heat, cold, etc.) and nearby personnel from rotating mechanical parts of antennas and streamlining antennas to reduce aerodynamic drag and to conceal antennas from public view. Metamaterials are artificial materials with a great potential for antenna design, and many studies explore applications of metamaterials to antennas but just a few to the design of radomes. This paper discusses the possibilities that metamaterials open up in the design of microwave radomes and introduces the concept of metaradomes. The use of metamaterials can improve or correct characteristics (gain, directivity, and bandwidth) of the enclosed antenna and add new features, like band-pass frequency behavior, polarization transformations, the ability to be switched on/off, and so forth. Examples of applications of metamaterials in the design of microwave radomes available in the literature as well as potential applications, advantages, drawbacks, and still open problems are described.