Because of the ultrafast and photon-driven nature of the transport in their active region, we demonstrate that quantum cascade lasers can be operated as resonantly amplified terahertz detectors with wide RF bandwidth. Tunable responsivities up to 50 V/W and noise equivalent powers down to 100 pW/Hz1/2 are demonstrated at 4.7 THz. Constant peak responsivities with respect to the detector temperature are observed up to 80 K. Thanks to the ≈ps intersub-band lifetime, electrical bandwidths larger than 20 GHz can be obtained, allowing the detection of optical beatnotes from quantum cascade THz frequency combs.