In low dimensional systems, electron correlation effects can often be enhanced. This can be vital since these effects not only play an important role in the study of many-electron physics, but are also useful in designing new materials for various applications. Since its isolation from graphite in 2004, graphene, a two dimensional sheet of carbon atoms, has drawn considerable interest due to its remarkable properties. In the past few years, research has moved on from single to bi-, dual- and multi-layer graphene systems, each displaying their own multitudes of intriguing properties. In particular, multi-layer systems that are electronically decoupled, but still coupled via the long-range Coulomb interaction, are very fascinating as they provide an opportunities to study phenomena like excitonic condensates, non-zero band gaps and van der Waals (vdW) interactions. In this thesis, I shall discuss our recent work on two different physical aspects of dual- layer graphene systems under uniaxial strain. Firstly, I shall present results on the vdW correlation energy evaluated, within the Random Phase Approximation, at zero temperature between two undoped graphene layers separated by a finite distance. The correlation energy is obtained for three anisotropic models with variations in the strength of the effective coupling constant. We find that the vdW interaction energy increases with increasing anisotropy and the many-body contributions to the correlation energy are non-negligible. In the second part, I shall talk about the formation of inter-layer electron-hole (excitonic) pairings, caused by the inter-layer Coulomb interaction between two uniaxially strained graphene sheets which are appropriately doped with electrons/holes and our studies of the dependence of strain on the effective interaction. We find that strain, in combination with precise control of the initial momentum can effectively overcome the suppression due to inter-layer screening effects.