My thesis describes new instrumentation and signal processing techniques developed for time-domain studies of the radio sky and applies these techniques to a variety of radio astronomical data. Time-domain algorithms were developed for the SERENDIP V survey, a commensal SETI survey operating at the Arecibo Observatory. Along with collaborators at the University of California at Berkeley, I helped develop the high frequency resolution digital FFT spectrometers used to collected the data. No signal with the characteristics of being from an extraterrestrial intelligence was observed. A method for automatically classifying broadband and narrowband signals in raw frequency-time data is presented. It uses both the first and second moments of a spectrum to characterize the how broad or narrowband a signal is. Our applications of this technique to real data show that this algorithm is an effective tool for radio frequency interference excision. A survey for rare, bright radio transients was undertaken with a 3.8 m radio telescope on the roof of the Space Sciences Building on Cornell's campus. This survey involved the end-to-end development of the hardware, software, and data analysis. The data were searched from single, dispersed pulses, but none were found. Multi-frequency observations of the eclipsing, binary white dwarf system J0651 were conducted at the Arecibo Observatory to search for variable emission, both short-duration, "burst-like" and periodic emission. The system has an orbital period of only 12.75 min, and this fast ro- tation may generate radio emission if the stars are magnetic, but no emission was seen. Five new pulsars, including three Rotating Radio Transients (RRATs), were discovered in a single pulse analysis of 23 months of Pulsar ALFA (PALFA) data collected with the Mock spectrometers. We expanded the existing pipeline to include several new algorithms, including the spectral modulation index and a single pulse rating. In addition to the new discoveries, forty-seven previously known pulsars were redetected. From this work I conclude that considering the time domain is key to fully understanding the radio sky. Time-domain studies require special algorithms and instrumentation and particular attention must be made to managing radio frequency interference.