PbS quantum dots (QDs), among the most mature nanocrystals obtained by colloidal chemistry, are promising candidates in optoelectronic applications at various operational frequencies. QD device performances are often determined by charge transport, either carrier injection before photoemission or charge detection after photoabsorption, which is significantly influenced by the dielectric environment. Here, we present the electronic structure and the optical gap of PbS QDs versus size for various solvents calculated using ab initio methods including the many-body perturbation approaches. This study highlights the importance of the dielectric environment, pointing out 1) the non-negligible shift of the electronic structure due to the ground state polarization; 2) a substantial impact on the electronic bandgap. The electron-hole binding energy, which varies largely with the QD size and solvent, is well-described by 1 an electrostatic model. This study reveals the fundamental physics of size and solvation effects, which could be useful to design PbS QDs-based optoelectronic devices.