Molecular dynamics simulations were used to probe mixtures of ionic liquids (ILs) with common molecular solvents. Four types of systems were considered: (i) 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide plus benzene, hexafluorobenzene or 1,2-difluorobenzene mixtures; (ii) choline-based ILs plus ether mixtures (iii) choline-based ILs plus n-alkanol mixtures; and (iv) 1-butyl-3-methylimidazolium nitrate and 1-ethyl-3-methylimidazolium ethyl sulfate aqueous mixtures. The results produced a wealth of structural and aggregation information that highlight the resilience of the polar network of the ILs (formed by clusters of alternating ions and counter-ions) to the addition of different types of molecular solvent. The analysis of the MD data also shows that the intricate balance between different types of interaction (electrostatic, van der Waals, H-bond-like) between the different species present in the mixtures has a profound effect on the morphology of the mixtures at a mesoscopic scale. In the case of the IL aqueous solutions, the present results suggest an alternative interpretation for very recently published x-ray and neutron diffraction data on similar systems.