Graphite-like 2D nanolattices of dielectrics and semiconductors with enhanced anisotropic electronic properties are good candidates to pave the way to the ultimate scaling and performances of future nanoelectronic devices. Graphene, the most studied representative of the 2D graphitic materials, has overshadowed research on other potential 2D nanolattices with totally unexplored physical properties. One such 2D lattice, silicene (germanene), the Si (Ge) sp2-hybridized equivalent of graphene, if it exists, may offer better compatibility with silicon processing and may provide solutions for some of the problems of graphene associated with the lack of an energy gap. In this proposal we will focus on finding ways to induce and stabilize sp2 hybridization in Si and Ge and prove for the first time that silicene has a physical existence. This should be combined with similarly sp2-hybridized dielectrics which could offer a template for silicene and germanene growth and, at the same time, serve as gate insulators which are necessary for charge and current control in the 2D semiconductors. The ideal situation would be to obtain a sequence of sp2-hybridized dielectric/silicene alternating monolayers which are weakly bonded between each other in the vertical direction via van der Waals forces. A strong anisotropy could also be induced by regular sp3-hybridized ultrathin Si and Ge in which the periodicity along the vertical growth direction is artificially broken by the insertion of monolayer-thick non- semiconducting layers. In such a case, the bandstructure and the density of states could be strongly modified reducing in-plane effective mass while inhibiting the transport perpendicular to the layers. This could reduce gate leakage and carrier scattering, thus maintaining high mobility at low equivalent oxide thickness.