The COBRA experiment is searching for neutrinoless double beta decay using CdZnTe semiconductor detectors. The main focus is on Cd-116, with a decay energy of 2814 keV well above the highest naturally occurring gamma lines. Furthermore, Te-130, with a high natural abundance, and Cd-106, a double β⁺ emitter, are under investigation. Advantageous is the possibility to operate the detectors at room temperature. Besides coplanar grid detectors, pixelised detectors are considered. The latter ones would allow for particle discrimination, therefore providing efficient background reduction. The current status of the experiment is described, including the upgrade of the R&D set-up in spring 2011 at the LNGS underground laboratory, the different detector concepts and the latest half-life limits. Furthermore, studies on the use of liquid scintillator for background suppression and Monte Carlo simulations are presented.