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The development of methods and algorithms to solve the $N$-body problem for classical, collisionless, non-relativistic particles has made it possible to follow the growth and evolution of cosmic dark matter structures over most of the Universes history. In the best studied case $-$ the cold dark matter or CDM model $-$ the dark matter is assumed to consist of elementary particles that had negligible thermal velocities at early times. Progress over the past three decades has led to a nearly complete description of the assembly, structure and spatial distribution of dark matter haloes, and their substructure in this model, over almost the entire mass range of astronomical objects. On scales of galaxies and above, predictions from this standard CDM model have been shown to provide a remarkably good match to a wide variety of astronomical data over a large range of epochs, from the temperature structure of the cosmic background radiation to the large-scale distribution of galaxies. The frontier in this field has shifted to the relatively unexplored subgalactic scales, the domain of the central regions of massive haloes, and that of low-mass haloes and subhaloes, where potentially fundamental questions remain. Answering them may require: (i) the effect of known but uncertain baryonic processes (involving gas and stars), and/or (ii) alternative models with new dark matter physics. Here we present a review of the field, focusing on our current understanding of dark matter structure from $N$-body simulations and on the challenges ahead.
We present N-body simulations of a new class of self-interacting dark matter models, which do not violate any astrophysical constraints due to a non-power-law velocity dependence of the transfer cross section which is motivated by a Yukawa-like new g
We study the shapes of subhalo distributions from four dark-matter-only simulations of Milky Way type haloes. Comparing the shapes derived from the subhalo distributions at high resolution to those of the underlying dark matter fields we find the for
Predicting the spatial distribution of objects as a function of cosmology is an essential ingredient for the exploitation of future galaxy surveys. In this paper we show that a specially-designed suite of gravity-only simulations together with cosmol
The presence of substructures in dark matter haloes is an unavoidable consequence of the cold dark matter paradigm. Indirect signals from these objects have been extensively searched for with cosmic rays and gamma-rays. At first sight, Cherenkov tele
We simulate the growth of isolated dark matter haloes from self-similar and spherically symmetric initial conditions. Our N-body code integrates the geodesic deviation equation in order to track the streams and caustics associated with individual sim