Tunka-Rex is a $3\,$km$^2$ large antenna array for cosmic-ray air showers at the TAIGA observatory (Tunka Advanced Instrument for cosmic ray physics and Gamma Astronomy) in Siberia close to Lake Baikal. In autumn 2016 Tunka-Rex has been extended to a total of 63 stations, each equipped with SALLA antennas for two polarization directions operating in the band of $30-80\,$MHz. All antenna stations are triggered by the other cosmic-ray detectors at the site, i.e., Tunka-Rex runs in coincidence with the Tunka-Grande array of scintillation detectors and during clear nights additionally in coincidence with the Tunka-133 non-imaging air-Cherenkov array. Compared to previous measurements, the day-time and bad-weather trigger increases the annual exposure by an order of magnitude, and the higher density of antennas is expected to increase the accuracy - in particular for the cosmic-ray mass composition. In addition to the status and potential of Tunka-Rex an overview of recently published results will be presented: by comparing the radio and the air-Cherenkov signals of the same air showers, the Tunka-Rex precision for the most important shower parameters has been determined. The direction precision is about $1^\circ$, the precision for the depth of the shower maximum, $X_\mathrm{max}$, is better than $40\,$g/cm$^2$ for high-quality events, and the energy precision is better than $15\,\%$. A rough estimation of the shower energy and of $X_\mathrm{max}$ is even possible with only a single antenna station when using the shower geometry measured by Tunka-133. Moreover, by using exactly the same external calibration source for the antennas as at the LOPES experiment we have shown that the absolute energy scale of different air-shower arrays can be compared with each other at $10\,\%$ precision. Thus, Tunka-Rex will improve the total accuracy of TAIGA for the energy as well as for the mass composition of cosmic rays of energy above $0.1\,$EeV.