The paper focuses on the dynamics of space debris in the Earth environment, with a celestial mechanics and theoretical point of view, and not with an operational perspective. The introduction describes the Earth space junk, with the description and the evolution of the debris population, and lists the main forces acting on them, their relative importance and the main regions of interest (Low, Medium and Geostationary Orbits, later called LEO, MEO and GEO). The resonances are present at several levels: gravitational resonances, for MEO and GEO, but also lunar-solar resonances, and secondary resonances involving the Sun. A classical Hamiltonian approach is proposed for GEO or MEO regions, with different associated toys models. The numerical integrations, their limits, their characteristics, symplectic or not, for short or long time integrations are presented, commented and compared, with the connected chaotic indicators (MEGNO in particular) which allow to put the stability of some regions into perspective. The solar radiation pressure is investigated with more details, without or with shadowing effects especially in the GEO region. For the LEO, the atmospheric drag plays an important role on the dynamics, dependent on the ballistic coefficient. Some comparisons are presented, concerning the solar activity and the consequences on the reentry times. A few words about the rotation of the debris, the explosions and collisions mechanisms, and the possibility to simulate those events in a synthetic population conclude the paper.