A general formulation is presented for the gain, efficiency, and receiving cross section of antennas in a dissipative (homogeneous and isotropic) medium, and performance limits are established that are generally applicable to reciprocal antennas. The antenna is assumed to be encapsulated in a spherical enclosure immersed in a lossy medium. It is shown that the realized gain is proportional to the product of the directive gain and an efficiency factor, which for lossless antennas is a measure of only the dissipation associated with the near fields. An upper bound on this efficiency is in fact attainable by an elementary magnetic dipole. Since plane waves incident on antennas in dissipative media are frequently inhomogeneous, the definition of the receiving cross section is extended to include such waves. It is shown that for inhomogeneous plane wave incidence the wave received at the antenna terminals is proportional to a far field pattern quantity evaluated in the invisible region. These results are applied to antennas imbedded in a lossy half-space. The limitations on the receiving cross section and realized gain imposed by dissipation in the medium are considered. For a spherical enclosure of a given radius an upper bound is obtained on the receiving cross section. Moreover, this upper bound can be attained by a lossless antenna. Normalized curves of the maximum receiving cross section are plotted for several dissipation factors.