While optical and radio transient surveys have enjoyed a renaissance over the past decade, the dynamic infrared sky remains virtually unexplored. The infrared is a powerful tool for probing transient events in dusty regions that have high optical extinction, and for detecting the coolest of stars that are bright only at these wavelengths. The fundamental roadblocks in studying the infrared time-domain have been the overwhelmingly bright sky background (250 times brighter than optical) and the narrow field-of-view of infrared cameras (largest is 0.6 sq deg). To begin to address these challenges and open a new observational window in the infrared, we present Palomar Gattini-IR: a 25 sq degree, 300mm aperture, infrared telescope at Palomar Observatory that surveys the entire accessible sky (20,000 sq deg) to a depth of 16.4 AB mag (J band, 1.25um) every night. Palomar Gattini-IR is wider in area than every existing infrared camera by more than a factor of 40 and is able to survey large areas of sky multiple times. We anticipate the potential for otherwise infeasible discoveries, including, for example, the elusive electromagnetic counterparts to gravitational wave detections. With dedicated hardware in hand, and a F/1.44 telescope available commercially and cost-effectively, Palomar Gattini-IR will be on-sky in early 2017 and will survey the entire accessible sky every night for two years. Palomar Gattini-IR will pave the way for a dual hemisphere, infrared-optimized, ultra-wide field high cadence machine called Turbo Gattini-IR. To take advantage of the low sky background at 2.5 um, two identical systems will be located at the polar sites of the South Pole, Antarctica and near Eureka on Ellesmere Island, Canada. Turbo Gattini-IR will survey 15,000 sq. degrees to a depth of 20AB, the same depth of the VISTA VHS survey, every 2 hours with a survey efficiency of 97%.