Lasers　emitting　visible　light　based　on　high　harmonic　generation　(HHG)　have　significantly　enhanced　measurement　capabilities,　enabling　new　applications　across　precision　metrology,　attosecond　science,　and　ultrafast　time-resolved　spectroscopy.　This　paper　discusses　the　theoretical　framework　of　HHG　with　a　focus　on　nonlinear　effects,　examining　in　depth　second-harmonic　generation　(SHG)　and　third-harmonic　generation　(THG)　mechanisms,　as　well　as　a　thermal　nonlinear　model　for　pump　stability　analysis.　The　current　state　of　HHG　within　integrated　optical　circuits　is　reviewed,　with　a　particular　emphasis　on　its　implementation　in　high-index　doped　silica　glass　micro-ring　resonators　(HDSG　MRRs).　We　conclude　by　addressing　future　directions　for　optimizing　these　systems　to　expand　their　applicability　in　advanced　photonic　technologies,　highlighting　their　potential　for　innovation　in　both　applied　and　fundamental　sciences.