The magnetopause is a current sheet forming the boundary between the geomagnetic field on one side and the shocked solar wind on the other side. This paper discusses properties of the low-latitude dawn and dusk flanks of the magnetopause. The reported results are based on a large number of measurements obtained by the Cluster satellites during magnetopause traversals. Using a combination of single-spacecraft and multispacecraft techniques, we calculated macroscopic features such as thickness, location, and motion of the magnetopause. The results show that the typical flank magnetopause is significantly thicker than the dayside magnetopause and also possesses a pronounced and persistent dawn-dusk asymmetry. Thicknesses vary from 150 to 5000 km, with an median thickness of around 1400 km at dawn and around 1150 km at dusk. Current densities are on average higher on dusk, suggesting that the total current at dawn and dusk are similar. Solar wind conditions and the interplanetary magnetic field cannot fully explain the observed dawn-dusk asymmetry. For a number of crossings we were also able to derive detailed current density profiles. The profiles show that the magnetopause often consists of two or more adjacent current sheets, each current sheet typically several ion gyroradii thick and often with different current direction. This demonstrates that the flank magnetopause has a structure that is more complex than the thin, one-dimensional current sheet described by a Chapman-Ferraro layer.