Complex optical pulse shapes are typically generated from ultrashort laser pulses by manipulating the optical spectrum of the input pulses. This generates complex but periodic time-domain waveforms. Optical Arbitrary Waveform Generation (OAWG) builds on the techniques of ultrashort pulse-shaping, with the goal of making non-periodic, truly arbitrary optical waveforms. Some applications of OAWG are coherently controlling chemical reactions on a femtosecond time scale, improving the performance of LADAR systems, high-capacity optical telecommunications and ultra wideband signals processing. In this work, an array of Vertical Cavity Surface Emitting Lasers (VCSELs) are used as modulators, by injection-locking each VCSEL to an individual combline from an optical frequency comb source. Injection-locking ensures that the VCSELs' emission is phase coherent with the input combline, and modulating its current modulates mainly the output optical phase. The multi-GHz modulation bandwidth of VCSELs updates the output optical pulse shape on a pulse-to-pulse time scale, which is an important step towards true OAWG. In comparison, it is about a million times faster than the liquid-crystal modulator arrays typically used for pulse shaping! Novel components and subsystems of Optical Arbitrary Waveform Generation (OAWG) are developed and demonstrated in this work. They include: 1. Modulators An array of VCSELs is packaged and characterized for use as a modulator for rapid?update pulse?shaping at GHz rates. The amplitude and phase modulation characteristics of an injection-locked VCSEL are simultaneously measured at GHz modulation rates. 2. Optical Frequency Comb Sources An actively mode-locked semiconductor laser was assembled, with a 12.5 GHz repetition rate, ~ 200 individually resolvable comblines directly out of the laser, and high frequency stability. In addition, optical frequency comb sources are generated by modulation of a single frequency laser. 3. High-resolution optical spectral demultiplexers The demultiplexers are implemented using bulk optics, and are used to spatially resolve individual optical comblines onto the modulator array. 4. Optical waveform measurement techniques Several techniques are used to measure generated waveforms, especially for spectral phase measurements, including multi-heterodyne phase retrieval. In addition, an architecture for discriminating between ultrashort encoded optical pulses with record high sensitivity is demonstrated.