This　paper　aims　to　present　a　comprehensive　survey　on　water　quality　soft-sensing　of　a　wastewater　treatment　process　(WWTP)　based　on　artificial　neural　networks　(ANNs).　We　mainly　present　problem　formulation　of　water　quality　soft-sensing,　common　soft-sensing　models,　practical　soft-sensing　examples　and　discussion　on　the　performance　of　soft-sensing　models.　In　details,　problem　formulation　includes　characteristic　analysis　and　modeling　principle　of　water　quality　soft-sensing.　The　common　soft-sensing　models　mainly　include　a　back-propagation　neural　network,　radial　basis　function　neural　network,　fuzzy　neural　network　(FNN),　echo　state　network　(ESN),　growing　deep　belief　network　and　deep　belief　network　with　event-triggered　learning　(DBN-EL).　They　are　compared　in　terms　of　accuracy,　efficiency　and　computational　complexity　with　partial-least-square-regression　DBN　(PLSR-DBN),　growing　ESN,　sparse　deep　belief　FNN,　self-organizing　DBN,　wavelet-ANN　and　self-organizing　cascade　neural　network　(SCNN).　In　addition,　this　paper　generally　discusses　and　explains　what　factors　affect　the　accuracy　of　the　ANNs-based　soft-sensing　models.　Finally,　this　paper　points　out　several　challenges　in　soft-sensing　models　of　WWTP,　which　may　be　helpful　for　researchers　and　practitioner　to　explore　the　future　solutions　for　their　particular　applications.