In this thesis, based on the first-principles density functional theory simulation, we analyze the properties of graphene-based materials with dopants and defects and understand chemical reactions such as gas adsorption, desorption and electrochemical catalysis. Understanding and controlling atomic dopants and defects are significant because they can affect to the material properties and act as a catalytic active site. Herein, we focus on nitrogen dopants and divacancy defects in graphene-based materials. It was confirmed that the divacancy defects in graphene, which can have various configurations depending on the nitrogen content, have different favorable atoms to bind. Especially, group Ⅳ elements easily formed divacancy defect complexes in nitrogen-poor environment, while, in nitrogen-rich condition, divalent transition metals can bind with double vacancy defects easily. Their electronic structure and catalytic activity vary sensitively depending on nitrogen content, and Ni and Cu defects can be replaced to Fe or Co defects known as a good catalyst by electrochemical cation exchange reaction. In addition, NH3 adsorption energy was examined to compare the catalytic activity of divacancy defects containing transition metal single atoms and dimers. The early transition metals show better stability and catalytic activity than the late transition metals. Early transition metal embedded divacancy defects with a buckled atomic structure are expected to have superior catalytic efficiency because several molecules can be adsorb to the protruded single metal atom with relatively high binding strength. Also, the catalytic efficiency of various kinds of nitrogen dopants in carbon nanostructure was compared to determine the active sites for the oxygen evolution reaction (OER). As a result, nitrogen atoms at the unzipped edges directly participate as an important active site for the oxygen evolution reaction with lower overpotential than pyridinic and quaternary nitrogen.