The theoretical work carried out in this thesis presents the electrical properties of two different types of two terminal nanojunctions: one dealing with gold electrodes which form gold|molecule|gold structures and the other has carbon nanotube (CNT) electrodes forming CNT|molecule|CNT junctions. The theoretical tools employed are firstly, density functional theory (DFT). Chapter 2 presents an introduction to the theoretical concept of DFT and in this work the implemented version used, namely the SIESTA code. The second tool is the quantum transport code GOLLUM. To introduce this technique in Chapter 3, I present solutions of Green’s functions for infinite and semi-infinite chains and the transmission