Abstract：Due to the theoretical discovery of asymptotic freedom for the strong interaction (a fundamental interaction) and later experimental confirmations, three American theoretical physicists (David J. Gross, Frank Wilczek and H. David Politzer) have awarded the Nobel Prize in Physics 2004. The elementary elements to establish the Quantum Chromodynamics (QCD), the theory for the strong interaction, are briefly reviewed according to history. How to reach to the asymptotic freedom for Yang-Mills theories is introduced and its physics meaning in QCD is explained. The latest and essential experimental tests of the asymptotic freedom are presented, and from the presentation one may conclude that the theoretical prediction of the asymptotic freedom consists with experimental measurements excellently. The perturbative QCD, which is rooted to the asymptotic freedom, is outlined. It is pointed out that the theoretical discovery and the experimental confirmations of the asymptotic freedom are crucial ...更多for QCD to be the right theory of the strong interaction and some frontiers of QCD, such as 'color confinement', etc., are listed. The discovery indeed has deeply affected particle physics, such as the Standard Model with QCD as one of the main contents and to lead to the so-called Grand Unification Theories (GUTs) for strong and electroweak interactions etc..