A technology for accurate generation and characterization of arbitrary optical waveforms scaling to terahertz bandwidth can fundamentally transform modern applications including optical spectroscopy, communications, imaging, and many others. Generation of terahertz bandwidth optical waveforms is challenging because direct electrical-to-optical modulation schemes have bandwidths below 100 GHz due to limitations in current electronic technologies. Similarly, continuous, real-time amplitude and phase characterization of optical waveforms is currently limited to tens of gigahertz. Novel methods which take advantage of frequency multiplexing or temporal multiplexing techniques are necessary to extend the generation and measurement bandwidths. This dissertation focuses on bandwidth-scalable optical arbitrary waveform generation based on a frequency-multiplexed technique using optical frequency combs. Three components are necessary for waveform generation: an optical frequency comb which provides a set of evenly and precisely spaced optical frequencies spanning several terahertz, an optical multiplexer and demultiplexer pair to isolate and combine individual spectral lines, and an array of modulators. Frequency-parallel modulation on each comb line broadens the spectrum of each line to fill the spectral gaps between the lines. Defining the signals applied to each modulator enables synthesis of a continuous and fully specified optical spectrum spanning the entire frequency comb's bandwidth. Full control over the spectrum allows complete specification of the temporal domain waveform via the Fourier transform. Optical arbitrary waveform measurement is a symmetric technique where the signal spectrum is demultiplexed into spectral slices and then each spectral slice is coherently detected with respect to a reference comb line. This dissertation introduces a theory for, and shows demonstrations of, the generation and measurement of optical arbitrary waveforms that are scalable to terahertz bandwidths. Results include high-fidelity generation and measurement of arbitrary shaped optical frequency combs with 10, 20, and 40 GHz comb line spacing using integrated waveform shapers. Single-shot waveform measurements show near quantum-limited characterization across a 200-ps wide optical window with 500 GHz bandwidth. Additionally, an integrated real-time implementation of optical arbitrary waveform measurement demonstrates continuous characterization of 160 GHz bandwidth optical waveforms with a 2 s duration. Terahertz-bandwidth, continuous arbitrary optical waveform generation and measurement provide a unique functionality, which will fundamentally impact many fields of science.