HERA-B is a fixed target experiment working on the 920 GeV proton beam of the HERA accelerator at the DESY laboratory in Hamburg. During the last data taking period (2002-2003), about 150 million dilepton triggers, 220 million minimum bias events and 35 million hard photon triggers were acquired. These large statistics allow detailed studies on the production of charmonium states in proton-nucleus p-A collisions, which extend for the first time into the negative Feynman-x (xF) region. Measurements of the inclusive b (b) over bar. and open charm cross sections are also ongoing. After a brief discussion of the detector and of the data samples, we report on preliminary results obtained on these physics topics.