Abstract: The structural and electronic properties of silicene and germanene on metallic and non-metallic substrates are investigated theoretically, using first-principles simulations. We first study the interaction of silicene with Ag(111) surfaces, focusing on the (4x4) silicene/Ag structure. Due to symmetry breaking in the silicene layer (nonequivalent number of top and bottom Si atoms), silicene is predicted to be semiconducting, with a computed energy gap of about 0.3 eV. However, the charge transfer occurring at the silicene/Ag(111) interface leads to an overall metallic system. We next investigate the interaction of silicene and germanene with hexagonal non-metallic substrates, namely ZnS and ZnSe. On reconstructed (semiconducting) (0001) ZnS or ZnSe surfaces, silicene and germanene are found to be semiconducting. Remarkably, the nature (indirect or direct) and magnitude of their energy band gap can be controlled by an out-of-plane electric field.