This thesis investigates the three frontiers of superconducting radio frequency (SRF) science: Gradient, Continuous wave beam power, and High quality factor structures. On the first front, the full temperature dependence of the superheating field - which sets the ultimate gradient limit for SRF cavities was measured for the first time for niobium. It was found that the Ginsburg-Landau result near T c is consistent with measurements within measurement uncertainty to even low temperatures. The beam power frontier was extended by designing a multicell cavity for the Cornell Energy Recovery Linac (ERL) with strongly damped higher-order modes. Simulations show that an ERL constructed of these cavities can support high beam current in excess of 300 mA, ∼30 times higher than in ERLs currently in operation. Finally, measurements of the prototype main linac cavity for the Cornell ERL demonstrate that the fundamental accelerating mode of the cavity in a fully equipped cryomodule can achieve quality factors in excess of 6 × 1010 at 1.8 K and 16.2 MV/m, a result more than tripling the design specification. This prototype structure also set a world record of Q0 = 1 × 1011 at 1.6 K, for a cavity installed in a fully equipped cryomodule, and introduces the possibility of a new class of extremely high efficiency SRF accelerators.