The evolution of structure in the Universe is one of the hottest topics in Cosmology and Astrophysics. In the last years the so-called $\Lambda$-CDM-model could be established also with great help of very large computer simulations. This model describes a Universe that consists mainly of dark components: 96% are made of dark energy and dark matter. Ordinary matter made up of baryons give only 4% to the total content of the Universe. The talk will present recent results with the main focus on computational methods and challenges in that field. A state-of-the-art computer code for running these calculations will be presented in detail.