The trend over the last 50 years of down-scaling the silicon transistor to achieve faster computations has led to doubling of the number of transistors and computation speed over about every two years. However, this trend cannot be maintained due to the fundamental limitations of silicon as the main material for the semiconducting industry. Therefore, there is an active search for exploration of alternate materials. Among the possible candidates that can may be able to replace silicon is graphene which has recently gained the most attention. Unique properties of graphene include exceedingly high carrier mobility, tunable band gap, huge optical density of a monolayer, anomalous quantum Hall effect, and many others. To be suitable for microelectronic applications the material should be semiconductive, i.e. have a non-zero band gap. Pristine graphene is a semimetal, but by the virtue of doping the graphene surface with different molecules and radicals a band gap can be opened. Because the electronic properties of all materials are intimately related to their atomic structure, characterization of molecular and electronic structure of functionalizing groups is of high interest. The ab-inito (from the first principles) calculations provide a unique opportunity to study the influence of the dopants and thus allow exploration of the physical phenomena in functionalized graphene structures. This ability paves the road to probe the properties based on the intuitive structural information only. A great advantage of this approach lies in the opportunity for quick screening of various atomic structures. We conducted a series of ab-inito investigations of graphene functionalized with covalently and hapticly bound groups, and demonstrated possible practical usage of functionalized graphene for microelectronic and optical applications. This investigation showed that it is possible produce band gaps in graphene (i.e., produce semiconducting graphene) of about 1 eV, without degrading the carrier mobility. This was archived by considering the influence of those adducts on electronic band structure and conductivity properties.