Tunka-Rex, the Tunka radio extension, is an array of about 20 antennas currently under construction, which covers an area of 1 km2. Tunka-Rex measures the radio emission of cosmic-ray air showers above 1016 eV. It is triggered by the photomultipliers of the Tunka-133 experiment which simultaneously measure the Cherenkov light emitted by the same air showers. The radio-Cherenkov-hybrid measurements thus offer a unique opportunity for a cross-calibration of both detection methods. The main goal of Tunka-Rex is to determine the precision of the radio reconstruction for the energy and the atmospheric depth of the shower maximum, Xmax, and thus to experimentally test theoretical predictions that the radio precision can be similar to the precision of air-Cherenkov and fluorescence measurements. At the same time, Tunka-Rex can demonstrate that radio measurements can be performed on a large area for a relatively cheap price, since the antennas will be connected to the already existing Tunka DAQ. Finally, radio-antenna arrays have the perspective to increase the effective observation time compared to air-Cherenkov and fluorescence detectors by an order of magnitude, since radio measurements are possible under almost any atmospheric and light conditions.