The aim of the COBRA experiment is to prove the existence of neutrinoless double-beta-decay (0 β β -decay) and to measure its half-life. For this purpose a detector array made of cadmium-zinc-telluride (CdZnTe) semiconductor detectors is operated at the Gran Sasso Underground Laboratory (LNGS) in Italy. This setup is used to investigate the experimental issues of operating CdZnTe detectors in low-background mode and to identify potential background components, whilst additional studies are proceeding in surface laboratories. The experiment currently consists of monolithic, calorimetric detectors of coplanar grid design (CPG detectors). These detectors are 1 × 1 × 1 cm3 and are arranged in 4 × 4 detector layers. Ultimately four layers will be installed by the end of 2013, of which two are currently operating. To date 82.3 kg·days of data have been collected. In the region of interest for 116Cd around 2.8 MeV, the median energy resolution is 1.5% FWHM, and a background level near 1 counts/keV/kg/y has been reached. This paper gives an overview of the current status of the experiment and future perspectives.