Almost all the known mass of the universe can be attributed to nuclei, i.e. bound states of nucleons (protons and neutrons). These are made up of quarks and gluons, that strongly interact according to the laws of quantum chromodynamics (QCD). QCD constitutes the theoretically cleanest and most solid component of the present standard model of elementary particles and their (strong and electroweak) interactions. This "model" leaves many questions unanswered and we may well learn about yet to be discovered fundamental theories from studying its cleanest part, i.e. QCD. Experimental discovery of physics "beyond the standard model" requires theoretical predictions of QCD corrections to non-QCD processes, which is the main phenomenological motivation for solving QCD. In spite of this theory being well established since over four decades, relatively little is known even about the inner structure of the nucleon, which serves as the fundamental probe for new physics both in collider experiments and in dark matter detectors: Just computing the distribution of the proton mass amongst its partons amounts to solving a strongly coupled, relativistic, non-linear multi-body bound state problem. I will give a brief introduction into the research area and report on recent supercomputer simulations of QCD, discretized on a four-dimensional space-time grid (Lattice QCD). Tremendous progress has been achieved recently in the field, due to novel techniques and algorithms, in combination with an ever-increasing compute power.

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