By introducing unknown Level-Sets fields defined on contact interfaces, the Signorini-Moreau contact conditions and the Coulomb friction laws are written as equations. From this, a continuous weak-strong formulation of dynamic frictional contact problems is derived; the Level-Sets being the intrinsic contact unknown fields. The problem is then discretized by time, space and collocation schemes. Some numerical tests are carried out, showing the effectiveness of our global approach. The paper is ended by showing a promising application of the multiscale Arlequin method to contact-impact problems.