A variety of cryogenic sensor arrays can be read out by coupling each detector element to a microwave resonator whose resonant frequency changes in response to the physics signal. The use of microfabrication techniques and high Q superconducting resonators allows thousands of sensor elements to be multiplexed in this way, and then simultaneously read out through a single RF cable. The SMuRF electronics provide high dynamic range readout along with flux-ramp drive to reduce 1/f noise, and firmware controlled RF line tracking to reduce system nonlinearities. The hardware design supports up to 4000 sensors operating in a 4-8GHz frequency range in a single ATCA card, allowing compact high density systems. The initial target applications are RF SQUID multiplexed CMB telescopes and energy-resolving X-ray detectors; however the hardware will also support MKID and other cryogenic sensors for cryogenic particle detectors and other applications.