Given the interference avoidance capacity, high gain, and dynamical reconfigurability, phased array antennas (PAAs) have emerged as a key enabling technology for future broadband mobile applications. This is especially important at millimeter-wave (mm-wave) frequencies, where the high power consumption and significant path loss impose serious range constraints. However, at mm-wave frequencies the phase and amplitude control of the feeding currents of the PAA elements is not a trivial issue because electrical beamforming requires bulky devices and exhibits relatively narrow bandwidth. In order to overcome these limitations, different optical beamforming architectures have been presented. In this paper we review the basic principles of phased arrays and identify the main challenges, that is, integration of high-speed photodetectors with antenna elements and the efficient optical control of both amplitude and phase of the feeding current. After presenting the most important solutions found in the literature, we analyze the impact of the different noise sources on the PAA performance, giving some guidelines for the design of optically fed PAAs.