A brief tutorial on the picosecond photoconductive effect is given. The use of picosecond optoelectronics for the characterization of broadband antennas is described. In particular, the transient radiation properties of equiangular-spiral and exponentially tapered coplanar-strip antennas are discussed. The transient radiation behavior and the polarization and radiation patterns of these antennas are easily determined with this measurement technique, without the need for anechoic chambers. Applications of picosecond-duration transient electromagnetic radiation to filter measurements, materials measurements, and scattering studies are discussed.