Since the invention of quarks as constituents of hadrons we are puzzled by the question why quarks are confined inside of hadrons. Quantum Chromodynamics (QCD) is the generally accepted theory of quark dynamics. In the lattice formulation of QCD one can demonstrate that quarks are evidently confined - but the mechanism of quark confinement is still under intensive discussion.

In recent lattice calculations we were able to show, that there are strong indications that thick vortices are responsible for confinement in QCD. At the end of the seventies 't Hooft and others suggested the vortex model and the dual superconductor model of confinement. At that time it was not clear which model should be favored. In the last years we presented numerical evidence in favor of the center vortex theory of confinement. We now look at the thick vortices as the basic topological objects which lead to confinement. We want to investigate all properties of these vortices, including the methods to detect them, and explain different aspects of confinement using vortices.

Vortices provide us with a unified picture of confinement: The QCD vacuum is a ``medium'' with magnetic vortices. It is filled with randomly fluctuating quantized magnetic flux tubes, fusing and splitting permanently. In this way they form a huge cluster percolating the whole space-time. By those magnetic properties of the vacuum the electric flux originating in quarks is compressed to straight flux tubes leading to a linear rising quark antiquark potential and to confinement.