We　briefly　present　the　theoretical　framework　of　a　hierarchical　multi-scale　approach,　which　is　an　ab　initiobased　stochastic　method,　and　its　applications　to　several　chemical/physical　kinetic　processes　on　metallic　surfaces.　We　first　introduce　necessary　theoretical　basis　of　ab　initio　and　Monte　Carlo　(MC)　methods,　and　then　illustrate　different　Monte　Carlo　algorithms　for　important　ensembles,　including　canonical　and　grand　canonical　ensembles.　In　the　following　section,　we　describe　two　important　protocols　which　are　essential　to　integrate　ab　initio　data　and　MC　models.　Two　examples　are　presented　in　order　to　elucidate　the　power　of　this　multi-scale　approach.　The　first　example　focuses　on　the　combination　of　kinetic　Monte　Carlo　and　transition　state　theory.　We　discuss　the　detailed　processes　of　performing　kinetic　Monte　Carlo　simulation　on　atomic　diffusion　on　alloyed　surface,　including　some　technical　aspects.　In　the　second　example,　we　presents　a　different　way　to　account　for　the　local　environment-sensitive　metal-catalyzed　O2　dissociation　reactions　using　combinatory　techniques　including　cluster　expansion　and　grand　canonical　Monte　Carlo　methods.　This　approach　provides　steady-state　rates　and　rate　derivatives　that　are　comparable　with　experiments.　Moreover,　the　connection　between　the　feasible　mechanisms　and　the　observed　kinetic　behaviors　can　now　be　built.　©　2016　by　IGI　Global.　All　rights　reserved.