All over the world an increase in the use of renewable energy sources is being sought, and here the utilisation of wind energy plays an important role. Germany currently represents one of the world's largest markets for wind energy. At the end of 2013, nearly 24 000 onshore wind turbines with a total output of approximately 34 000 MW had been installed in Germany. Hub heights of up to 140 m and outputs of 3 to 4 MW are now no longer unusual features of new onshore wind turbines. The focus of this paper is on concrete support structures for wind turbines. Different concrete tower concepts are presented, and the influence of the construction method on the design and verification processes is described. In particular, the text deals with the eigenfrequency analysis, as well as the bearing, shear and torsional resistances of concrete towers. The differences between cast-in-place and precast towers are listed.