In this thesis we study the effects of the interaction between electrons and phonon modes in condensed matter systems. We explore two theoretical outcomes of theelectron-phonon interaction: Charge wave order and superconductivity. The main aims of this thesis are to establish ways of making graphitic materials useful for digital computing, and to investigate unconventional forms of superconductivity. Low order perturbation theory is combined with a Green's function analysis to calculate electron band gaps in a bilayer graphitic material that. forms electron-phonon interactions via an adjacent polarisable substrate. Self-consistent equations are derived and computationally solved to examine band gap enhancement in bilayer graphene and bilayer boron nitride. We also compare results for several different systems to identify the most promising ones for future developments. Our results show a promising new method of gap creation, for gaps of up to leV, in a simple bilayer graphene system where the electron-phonon interaction causes enhanced charge density wave order. The possibility of three-dimensional high temperature bipolaronic superconductivity is examined numerically through continuous-time quantum Monte Carlo simulations backed up by an exact analytical approximation for large phonon-frequency. Bose-Einstein condensation of bipolarons in a cubic system is estimated to occur at temperatures as high as 90-120K at low carrier concentrations, where bipolarons are small and mobile. We also develop formalism for calculating the superconducting band gap of BCS like superconductivity in intercalated graphitic materials (IGMs). Green's function analysis combined with low order perturbation theory is used to derive a set of generalised self-consistent equations designed to accommodate the tight binding parameters of all IGMs.