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We present our work in optical generation of arbitrarily shaped millimeter-wave electromagnetic waveforms. Through a novel technique, which utilizes tailored optical pulse sequences from a direct space-to-time pulse shaper to drive a high-speed optical-to-electrical converter, we generate amplitude-equalized, arbitrarily phase- and frequency-modulated waveforms at center frequencies approaching 50 GHz. In addition, we demonstrate the extension of this technique to generation of arbitrary electromagnetic waveforms in the low-gigahertz range, through dispersive stretching of the pulse shaper output. In the dispersively stretched configuration, the duration of our electrical waveforms is tuned through simple alignment changes in our pulse-shaping apparatus.