Although the detection of light at terahertz (THz) frequencies is important for a large range of applications, current detectors typically have several disadvantages in terms of sensitivity, speed, operating temperature, and spectral range. Here, we use graphene as a photoactive material to overcome all of these limitations in one device. We introduce a novel detector for terahertz radiation that exploits the photothermoelectric (PTE) effect, based on a design that employs a dual-gated, dipolar antenna with a gap of similar to 100 nm. This narrow-gap antenna simultaneously creates a pn junction in a graphene channel located above the antenna and strongly concentrates the incoming radiation at this pn junction, where the photoresponse is created. We demonstrate that this novel detector has an excellent sensitivity, with a noise-equivalent power of 80 pW/root Hz at room temperature, a response time below 30 ns (setup-limited), a high dynamic range (linear power dependence over more than 3 orders of magnitude) and broadband operation (measured range 1.8-4.2 THz, antenna-limited), which fulfills a combination that is currently missing in the state-of-the-art detectors. Importantly, on the basis of the agreement we obtained between experiment, analytical model, and numerical simulations, we have reached a solid understanding of how the PTE effect gives rise to a THz-induced photoresponse, which is very valuable for further detector optimization.