After the first synthesis of carbon nanotubes by Iijima more than a decade ago, other types of nanotubes have been predicted and experimentally observed such as GaN, BN, and AlN among others. However, it was not until fairly recent that the most obvious alternative candidate for creating graphene-like sheets and nanotubes was proposed: Si. The present work is a theoretical study of the electronic properties of novel Silicon-based nanostrucutres, namely, Si graphene like structures and Si nanotubes. In order to do so, this dissertation begins with a review of the one- and multi-band empirical tight-binding theory and applies it to zincblende and diamond structures as applications of this model. In addition, a review of the electronic and structural properties of the Si predecessors (graphene and carbon nanotubes) is provided. Finally, this text provides a new tight-binding model that can account for the electronic properties of these structures. We considered the sp3s* and sp3 models up to first-and second-nearest neighbors, respectively. In addition, the effective masses of Si nanotubes are computed and compared to their carbon counterparts within the effective-mass scheme.