Numerical simulations have a prime role in modern cosmology. In this talk I will review the state-of-the-art in the field, discussing the importance of dark matter N-body simulations in our understanding of the dark universe. In the first part of the talk, I will pay attention to the challenges and recent developments in solving the N-body problem. In the second part of the talk, I'll discuss how these simulations can be used to perform the most accurate cosmological exploitation of the next generation of wide-field surveys.