Basements are often cold and damp, so beefing up insulation and good air-sealing makes the space more usable and livable. First we insulated from the inside, with interior insulation it is important for areas that likely to be subject to hydrostatic pressure (water — think more than 12″ below grade) to have vapor permeable insulation, otherwise there is a risk of condensation getting trapped behind it causing mold. For this we used regular white XPS. For the higher layer we used foil faced polyisocyanurate. Because both are fire hazards they are behind gypsum board.
Two insulation types on interior of basement wall 
Spray foam where wires penetrate the exterior walls
