Recent advances in nanolithography have allowed shifting of the resonance frequency of antennas into the optical and visible wavelength range with potential applications, for example, in single molecule spectroscopy by fluorescence and directionality enhancement of molecules. Despite such great promise, the analytical means to describe the properties of optical antennas is still lacking. As the phase velocity of currents at optical frequencies in metals is much below the speed of light, standard radio frequency (RF) antenna theory does not apply directly. For the fundamental linear wire antenna, we present an analytical description that overcomes this shortage and reveals profound differences between RF and plasmonic antennas. It is fully supported by apertureless scanning near-field optical microscope measurements and finite-difference time-domain simulations. This theory is a starting point for the development of analytical models of more complex antenna structures.