Here I describe several experiments that explore some of the rarest and most intriguing phenomena in the sky: short duration radio transients and possible electromagnetic emission from advanced extraterrestrial technology. Motivated by new discoveries and new technologies, we have performed, and are performing, some of the most thorough searches for these sources ever attempted. Our experiments include a "fly's eye" search for bright radio pulses at the Allen Telescope Array, commensal searches for extraterrestrial intelligence at the Arecibo Observatory, a targeted search of extrasolar planets for narrow-band radio emission using the Green Bank Telescope and an ongoing effort to discover pulsars in orbit around SgrA*. Although our experiments explore very different physics, they share common tools and techniques, notably a need for high performance digital signal processing. The experiments described here are prime examples of the synergy that exists between science and technology. Aided by dramatic advances in computing technology and the use of commodity components, we have enabled the processing of heretofore unheard of quantities of observational data. By taking advantage of a reusable design paradigm in which instruments do not have to be built from scratch, we have been able to develop new instruments quickly and efficiently. Our experiments are exploring wavelengths and signal types never before searched with high sensitivity, presenting the exciting chance for serendipitous discovery of unexpected phenomena. With an optimistic spirit, we venture into unexplored territory and expect the unexpected.This thesis is structured as follows: Chapter 1 presents an introduction to the scientific motivations for our experiments and the tools with which we conduct them, Chapter 2 describes our Fly's Eye Search for short duration radio transients at the Allen Telescope Array, Chapter 3 discusses our ongoing SETI experiments at radio and optical wavelengths and our plans for the future, Chapter 4 describes a 1.1-1.9 GHz search for narrow-band emission from planet candidates identified by the Kepler mission and Chapter 5 details our ongoing search for pulsars near Sgr A*.