The strong interactions of elementary particles are described theoretically in the framework of Quantum Chromodynamics (QCD). The solution of QCD is an outstanding problem in modern particle physics. The most promising way is given by numerical simulations using Monte Carlo Methods, in which the space-time continuum is replaced by a lattice. We shall demonstrate that since the invention of this approach by K. Wilson the conceptual, algorithmic and computer developments have progressed so much that today realistic simulations of lattice-QCD become possible, bringing us close to a, at least, numerical solution of QCD.