Meshes produced by thin metallic wires are widely used in antennas and microwave devices. Such regular two-dimensional structures provide unique electromagnetic properties strongly deepening on mesh parameters. Analysis of the mesh-containing antennas requires novel analytical solutions of many boundary problems. In the present review several solutions are discussed relating to reflector, microstrip and dipole antennas. In all the cases a small inter-wire spacing compared to the wavelength is assumed, which allows using the averaged boundary conditions method. The obtained radiation and matching antenna properties are discussed.