I will describe a brief history of discovery and some exciting recent developments in the world of pulsars and fast radio bursts. Pulsars, rapidly rotating highly magnetized neutron stars, were discovered in 1967 and continue to surprise and delight astronomers as powerful probes of fundamental physics and astrophysics. Fast radio bursts are millisecond-duration pulses of currently unknown origin that were discovered in 2007. Both pulsars and fast radio bursts have great promise at probing the universe on large scales and in fundamental ways. I will describe the science opportunities these phenomena present, and discuss the challenges and opportunities presented in their discovery.