Key dynamic processes at nano-scale, such as graphene hydrogenation and fluorination, and carbon nanotube (CNT) growth, cannot be observed in situ in real time. Nevertheless, such processes can be studied through complementary computational methods. This work simulates three important catalytic processes representing the growth of graphitic structures and functionalized graphene. The spillover phenomenon, which has been considered promising for efficient hydrogen storage, includes transfer of H from a metal catalyst to a graphitic receptor, to finally form a graphane island. Although, the spillover is energetically unfavorable to occur on pristine graphene, catalyst saturation provides a way for hydrogen adsorption on the receptor. Ab initio calculations show that the H chemical potential can be increased to a spillover favorable range. Unlike in graphane, upon graphene fluorination different stoichiometric phases form without a nucleation barrier, with the complete CF phase being thermodynamically most stable. After fluorination, graphene electronic properties are transformed from metallic to semiconducting. First-principles and tight-binding methods are used to investigate the patterning of nanoroads and quantum dots on these phases, combining metallic and semiconducting properties on the same sheet. In catalyzed CNT growth the metallic catalyst plays a fundamental role in cap nucleation. Such a mechanism cannot be seen in experiment, nor can it be simulated by first-principles due to its time-scale, yet it can be simulated through molecular dynamics. Tuning the metal-C interaction controls the condition for growth or encapsulation: Surface carbon-diffusion limits the growth below 600 K, and at higher temperatures they depend on cap lift-off. Such tuning can be done through catalyst alloying, as shown through ab initio simulations for Ni-Fe and Cu-Fe bimetallic catalysts. Catalyst shape also plays an important role in CNT growth. The minimization of the Ni surface energy defines the equilibrium crystal shape. Catalyst reshaping is analyzed through C adsorption by first-principles and reactive force fields. The Wulff-construction suggests a significant reduction of the surface energy anisotropy upon C adsorption, based on which a continuum phenomenological model that considers catalyst reshaping in CNT nucleation is formulated. This thesis explains the growth of graphitic structures and functionalized graphene at nano-scale through computational simulations.