This chapter introduces the reader to the modelling of particle-particle collisions. We assume that two spherical particles collide along the normal axis to plane of contact – that is, we only examine a head-on impact. In the beginning, attention is paid to the contact mechanics. The objective is therefore to prepare the reader for fundamental analysis. First, we investigate a simple case of a single force acting on a surface. This problem gradually extends to a similar contact between two spherical bodies (Hertz theory). Next, these bodies are allowed to move towards each other, and we observe their deformation – i.e., a head-on collision. The collision is also elastic, so there is no mechanical energy loss upon impact. Later, this issue is expanded upon by introducing dissipative forces during the contact in addition to the elastic forces discussed above. These dissipative forces are of different types: both linear and non-linear. Finally, another topic is introduced, which is plastic deformation. Here, the colliding bodies are allowed to deform permanently.