This dissertation is an observational exploration of the exciting physics that can be enabled by high-speed photometric monitoring of extremely low-mass (< 0.25 M[subscript sun symbol]) white dwarf stars, which are found in some of the most compact binaries known. It includes the cleanest indirect detection of gravitational waves at visible wavelengths, the discovery of pulsations in He-core WDs, the strongest evidence for excited p-mode pulsations in a WD, the discovery of the first tidally distorted WDs and their use to constrain the low-end of the WD mass-radius relationship, and the strongest cases of Doppler beaming observed in a binary system. It is the result of the more than 220 nights spent at McDonald Observatory doing high-speed photometry with the Argos instrument on the 2.1 m Otto Struve telescope, which has led to a number of additional exciting results, including the discovery of an intermediate timescale in the evolution of cooling DA WDs and the discovery of the most massive pulsating WD, which should have an ONe-core and should be highly crystallized. / text