Neutrons are born by fission at million electron-volts (MeV) energies, and they slow down (are “moderated”) by elastic and inelastic collisions with the materials in the reactor until they reach the thermal range below a few electron-volts (eV). In this range, in addition to losing energy in collisions, they can also gain energy by collisions with atoms and molecules in thermal motion. After some time, the distribution of the neutrons will come into equilibrium with the thermal motion of the atoms or molecules of the material and show a Maxwellian-like shapeMaxwelldistribution. In transport theory, a neutron is described completely by its position and velocity vector. The slowing down theory focuses mainly on energetical aspect and leaves aside the spatial aspect. This chapter covers essential concepts: the study of elastic collision, the neutron lethargy, the slowing down current.