In　the　machine　learning　fleld,　the　core　technique　of　artiflcial　intelligence,　reinforcement　learning　is　a　class　of　strategies　focusing　on　learning　during　the　interaction　process　between　machine　and　environment.　As　an　important　branch　of　reinforcement　learning,　the　adaptive　critic　technique　is　closely　related　to　dynamic　programming　and　optimization　design.　In　order　to　efiectively　solve　optimal　control　problems　of　complex　dynamical　systems,　the　adaptive　dynamic　programming　approach　was　proposed　by　combining　adaptive　critic,　dynamic　programming　with　artiflcial　neural　networks　and　has　been　attracted　extensive　attention.　Particularly,　great　progress　has　been　obtained　on　robust　adaptive　critic　control　design　with　uncertainties　and　disturbances.　Now,　it　has　been　regarded　as　a　necessary　outlet　to　construct　intelligent　learning　systems　and　achieve　true　brain-like　intelligence.　This　paper　presents　a　comprehensive　survey　on　the　learning-based　robust　adaptive　critic　control　theory　and　methods,　including　self-learning　robust　stabilization,　adaptive　trajectory　tracking,　event-driven　robust　control,　and　adaptive　H∞　control　design.　Therein,　it　covers　a　general　analysis　for　adaptive　critic　systems　in　terms　of　stability,　convergence,　optimality,　and　robustness.　In　addition,　considering　novel　techniques　such　as　artiflcial　intelligence,　big　data,　deep　learning,　and　knowledge　automation,　it　also　discusses　future　prospects　of　robust　adaptive　critic　control.　Copyright　©　2019　Acta　Automatica　Sinica.　All　rights　reserved.