In this article, we report on some of the fundamental chemical and physical processes responsible for the deposition of graphene by microwave plasma-enhanced chemical vapor deposition (PECVD). The graphene is grown by plasma decomposition of a methane and hydrogen mixture (CH 4 /H 2) at moderate pressures over polycrystalline metal catalysts. Different conditions obtained by varying the plasma power (300-400 W), total pressure (10-25 mbar), substrate temperature (700-1000°C), methane flow rate (1-10 sccm) and catalyst nature (Co-Cu) were experimentally analyzed using the in situ optical emission spectroscopy (OES) technique to assess the species rotational temperature of the plasma and the H-atom relative concentration. Then, two modeling approaches were developed to analyze the plasma environment during graphene growth. As a first approximation, the plasma is described by spatially averaged bulk properties, and the species compositions are determined using kinetic rates in the transient zero-dimensional (0D) configuration. The advantage of this approach lies in its small computational demands, which enable rapid evaluation of the effects of reactor conditions and permit the identification of dominant reactions and key species during graphene growth. This approach is useful for identifying the relevant set of species and reactions to consider in a higher-dimensional model. The reduced chemical scheme was then used within the self-consistent two-dimensional model (2D) to determine auto-coherently the electromagnetic field, gas and electron temperatures, heavy species, and electron and ion density distributions in the reactor. The 0D and 2D models are validated by comparison with experimental data obtained from atomic and molecular emission spectra.