The present paper describes modelization and discretization issues which seem to play an important role in the numerical modeling of contact problems in solid dynamics. The first aspect concerns subscale modeling, which is crucial when dealing with frictional contact. We will see how the use of one dimensional implicit thermomechanic models resolved in a subgrid inside each boundary cell leads to practical and physically accurate solutions. This model is controlled by the average velocity of the cell, but can reproduce the detailed aspect of the temperature field and elastoplastic strains in the interface layer. The next issue concerns time discretisation scheme. The proper approximation in time of elastic and contact efforts is a major issue in order to enforce energy conservation or persistency during contact in an exact or controlled way. We review in the paper a technique proposed in [1] which treats the contact by penalty and enforces energy correction techniques to all penalty and energy terms present in the problem formulation. A last key point concerns the treatment of inertia terms. The numerical solution of a dynamic contact problem often predicts contact pressures which have spurious oscillations both in space and in time at a scale related to the discretisation grid. As described in [2], the stability of standard algorithms and the regularity of the contact pressures is improved by introducing a modified mass matrix in which the nodes in potential contact will have no mass, the corresponding mass being affected to the neighboring internal elements. One can prove that this technique guarantees the regularity in time of the space discrete solution [2], and does not affect the convergence rate in the linear case. The numerical results to be presented indicate that these schemes are surprisingly good in practice. The authors would like to thank J.P. Perlat for many helpful discussions.