Ion-ion collisions are ubiquitous in high-energy physics. However, the electronic processes during these collisions are generally not well understood. The importance of investigating these fundamental collisional processes is demonstrated by the number of large undergoing experimental projects, such as for example DESIREE [1] or FISIC [2], involving several international groups. First principle calculations are obviously needed to complement these experimental efforts. During the talk, I will present the most recent progresses our group has achieved in the theoretical description of single and multiple electronic processes in ion-ion collisions. The non-perturbative methods we have developed and implemented in our group will be presented. Furthermore, I will present some illustrative and remarkable studies we have recently conducted thanks to these developments [3-7].