The thesis contains two parts. Part 1 describes the investigations on graphene and contains five sections. Section 1, gives a brief overview of graphene and other nanocarbons. The other four sections deal with various aspects of single-layer and few-layer graphene such as functionalization and solubilization, surface properties and gas adsorption, molecular charge transfer interaction and some properties and applications. Section 2 describes covalent and noncovalent functionalization and solubilization of few-layer graphene samples prepared by different methods as well as of single-walled carbon nanotubes (SWNTs). It includes covalent functionalization of graphene with organometallic reagents, noncovalent functionalization of graphene and SWNTs with surfactants as well as large aromatic molecules, and exfoliation of few-layer graphene by a water-soluble coronene carboxylate. Section 3 deals with surface properties and gas adsorption (mainly H2 and CO2) of few-layer graphenes. It is found that graphene samples with high surface area can adsorb even more than 3 wt% of H2 at high pressure which makes it promising material for gas-storage applications. Section 4 describes the molecular charge-transfer interaction of single and few-layered graphenes and SWNTs with different electron-donor and -acceptor molecules probed by both ITC measurements and Raman spectroscopy. Electron–acceptor molecules interact more strongly with graphene and SWNTs than the -donor molecules and nature of interaction of metallic SWNTs are different than the as-prepared ones. A Raman study of the interaction of single-layer graphene, prepared by micromechanical cleavage as well as chemical route, with an electron donor molecule such as tetrathiofulvalene (TTF) and an electron acceptor molecule such as tetracyanoethylene (TCNE) is examined. In Section 5, some properties and applications of graphene are discussed. These include fluorescence quenching phenomena observed with few-layer graphene samples on two fluorescent molecules such as coronene and perylene derivatives. Fabrication of a sensing device as well as of FETs prepared from doped and undoped few-layer and single-layer graphene samples forms part of this section. Part 2 of the thesis includes a brief introduction of hybrid open-framework material and synthesis, characterization and crystal structure of various open-framework metal carboxylates, starting with different transition and main group metals. The carboxylic acids used to form these frameworks vary such as simple aliphatic amino acids such as beta-alanine and aspartic acid or simple aliphatic hydroxyl carboxylic acid such as malic acid in its chiral and achiral forms or five-membered heterocyclic aromatic acid, such as imidazole dicarboxylic acid.