We present structure and dynamics of pure and doped with 0.25 mol LiTFSI N-methyl-N-propyl pyrrolidinium⁺TFSI^- (mppy⁺TFSI^-) and ethyl-methyl-imidazolium⁺TFSI^- ionic liquids. The liquid density, ion self-diffusion coefficients and conductivity predicted by MD simulations were found to be in good agreement with experimental data, where available. The Li⁺ cations were found to be coordinated on average by slightly less than four oxygen atoms with each oxygen atom being contributed by a different TFSI- anion in both imidazolium and pyrrolidinum-based ionic liquids.  Significant lithium aggregation through up to three TFSI^- anions bridging lithiums was observed (Li⁺…(O=S=O)_m…Li⁺), m=1,2,3, particularly at lower temperatures where the lithium aggregates were found to be stable for tens of nanoseconds. Polarization of TFSI^- anions is largely responsible for the formation of such lithium aggregates.  Li⁺ transport was found to occur primarily by exchange of TFSI^- anions in the first solvation shell with a smaller (~30%) contribution also due to Li⁺ cations diffusing together with their first solvation shell. Conductivity contribution due to the Li⁺ cation in LiTFSI doped mppy⁺TFSI^- ionic liquids was found to be greater than that for a model poly(ethylene oxide)(PEO)/LiTFSI polymer electrolyte but significantly lower than that for ethylene carbonate/LiTFSI liquid electrolyte.   Finally, the time-dependent shear modulus for the ionic liquids is compared with that for polymers and nonionic liquids