Adsorbates　on　metal　surfaces　are　typically　formed　from　the　dissociative　chemisorption　of　molecules　occurring　at　gas-solid　interfaces.　These　adsorbed　species　exhibit　unique　diffusion　behaviors　on　metal　surfaces,　which　are　influenced　by　their　translational　energy.　They　play　crucial　roles　in　various　fields,　including　heterogeneous　catalysis　and　corrosion.　This　review　examines　recent　theoretical　advancements　in　understanding　the　diffusion　dynamics　of　adsorbates　on　metal　surfaces,　with　a　specific　emphasis　on　hydrogen　and　oxygen　atoms.　The　diffusion　processes　of　adsorbates　on　metal　surfaces　involve　two　energy　transfer　mechanisms:　surface　phonons　and　electron-hole　pair　excitations.　This　review　also　surveys　new　theoretical　methods,　including　the　characterization　of　the　electron-hole　pair　excitation　within　electronic　friction　models,　the　acceleration　of　quantum　chemistry　calculations　through　machine　learning,　and　the　treatment　of　atomic　nuclear　motion　from　both　quantum　mechanical　and　classical　perspectives.　Furthermore,　this　review　offers　valuable　insights　into　how　energy　transfer,　nuclear　quantum　effects,　supercell　sizes,　and　the　topography　of　potential　energy　surfaces　impact　the　diffusion　behavior　of　hydrogen　and　oxygen　species　on　metal　surfaces.　Lastly,　some　preliminary　research　proposals　are　presented.　This　review　examines　recent　theoretical　advancements　in　understanding　the　diffusion　dynamics　of　adsorbates　on　metal　surfaces,　with　a　specific　emphasis　on　hydrogen　and　oxygen　atoms.　It　offers　valuable　insights　into　how　energy　transfer,　nuclear　quantum　effects,　supercell　sizes,　and　the　topography　of　potential　energy　surfaces　impact　the　diffusion　behavior　of　these　two　species.　image