Recent　advances　in　single-atom　alloy　(SAA)　catalysts　provide　a　unique　platform　for　understanding　spillover,　due　to　the　well-defined　nature　of　the　active　site　for　dissociative　chemisorption.　In　particular,　the　use　of　spilled　adsorbates　following　molecular　dissociation　on　the　host　metal　surface　facilitates　the　generation　of　high-value　chemicals　in　subsequent　catalytic　reactions.　Nevertheless,　the　factors　that　control　the　spillover　process　remain　to　be　fully　elucidated.　This　perspective　discusses　recent　theoretical　advances　in　the　spillover　dynamics　on　SAAs,　with　a　particular　focus　on　the　dissociation　and　spillover　processes　of　H-2　and　CH4.　It　provides　valuable　insights　into　how　various　factors,　such　as　energy　transfer,　nuclear　quantum　effects,　gas-adsorbate　interactions,　and　adsorbate　size,　impact　the　diffusion　behavior　of　hydrogen　and　methyl　species　on　SAA　surfaces.　The　article　concludes　with　a　discussion　of　future　prospects.　This　perspective　underscores　the　significance　of　spillover　dynamics　in　heterogeneous　catalysis,　with　important　implications　for　improving　catalytic　performance.