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. Tunable responsivities up to 50 V/W and noise equivalent powers down to 100 pW/sqrt(Hz) are demonstrated at 4.7 THz. Constant peak responsivities with respect to the detector temperature are observed up to 80K. Thanks to the sub-ps intersubband lifetime electrical bandwidths larger than 20 GHz can be obtained, allowing the detection of optical beatnotes from quantum cascade THz frequency combs.