Wolf-Rainer Hamann Title: Massive stars and their winds Abstract: Massive stars play an important role in the cosmos, e.g. as source of ionizing radiation and chemically enriched matter. Nevertheless, they are yet poorly understood. Mass loss by stellar winds is an essential driver of their evolution. Especially strong are the stellar winds from Wolf-Rayet stars. The spectral analysis of their emission-line spectra requires adequate non-LTE atmosphere models which account for the atmospheric expansion. We have developed such models and analyzed many stars in different environments, finding that the empirical results are partly in odds with the predictions from stellar evolution models. The problems become even worse with recent claims that the empirically mass-loss rates have been over-estimated and must be revised downwards, due to hitherto neglected effects of inhomogeneities in the stellar winds. Our studies, however, put such claims into question. Only recently, we succeeded in calculating hydrodynamically consistent WR models based on radiation pressure as their driving mechanism. However, it is not yet clear whether radiation pressure alone is sufficient for explaining all Wolf-Rayet subtypes.