Numerical simulations have played a crucial role in the development of modern
cosmology and in the establishment of LCDM. In this talk, I will review the main
results and the fundamental assumptions behind those dark matter simulations.
I will focus on the internal structure of halos and report on recent results on the
formation and evolution of the very first halos to form in cold dark matter cosmologies.
Then, I will discuss on recent attempts to model and study dark matter in the
continuum limit. I will show how such methods help to overcome known problems
of N-body simulations, and also how it is possible to get new insights into dark