This thesis presents experimental and related theoretical studies of single layer graphene, bilayer graphene and single walled carbon nanotubes. The thesis is divided into three parts; the first part describes the phonon renormalization due to doping in two dimensional graphene and one dimensional carbon nanotubes. In the recent years, there is a tremendous interest both experimentally and theoretically, in the issues related to electron-phonon coupling in nanotubes and graphene. Theoretically, it is expected that the presence of Kohn anomalies in graphene and metallic nanotubes will result in significant changes in the self energy of phonons due to doping. In particular, with Fermi energy shift how the blockage of phonon decay (due to Pauli Exclusion Principle) into electron-hole excitations changes the phonon frequencies as well as its life time have been studied in details in the first part of the thesis. Since in graphene and metallic nanotubes, the momentum relaxation time of electrons is comparable to the phonon pulsation time, the phonon cannot be treated as a static perturbation and hence non-adiabatic effects are taken into account using time dependent perturbation theory. Electron-phonon coupling constant is also a key parameter to understand the mobility of carrier due to electron scattering by optical phonons at room temperature and limitation of the maximum current carrying capacity of graphene and nanotubes. All these parameters are determined in the first part of the thesis by performing in-situ transport and Raman measurements on graphene and nanotubes based field effect transistors. The second part of the thesis deals with the interaction of bio-molecules (nucleobases) with the nanotubes and graphene. The binding energies of various nucleobases with nanotubes and graphene have been calculated theoretically using quantum chemical and classical force field calculations, and experimentally from isothermal titration (micro) calorimetry. In this part we also present an experimental study on the dynamics of water confined inside the carbon nanotubes. Proton nuclear magnetic resonance studies have been used to probe the freezing and dynamics of the confined water inside 1.4 nm diameter single walled carbon nanotubes. We have observed that the confined water does not freeze up to 223K. The dynamics of confined water has been studied using pulsed field gradient technique. The decay of spin echo intensity as a function of gradient field shows characteristic features of water confined in unidimensional channels. From the decay profiles the mean squared displacement of water molecules is obtained for different diffusive times, showing an unambiguous evidence of single file diffusion of water molecules inside the nanotubes i.e mean squared displacement varying as square root of time. In the last part, we have developed carbon nanotube based vibration sensor and accelerometer to detect the vibrations of liquid and solid, respectively, using the property of voltage generation in nanotubes due to liquid flow.