This paper presents a review of parametric models for video quality estimation standardized in the past few years. The focus of this paper is the estimation of quality degradation caused by the compression artifacts. The models introduced in the paper contain the work of Telecommunication Standardization Section of the International Telecommunication Union (ITU-T) Study Group 9 and Study Group 12, standardized as ITU-T Rec. G.1070, ITU-T Rec. P.1201 series, ITU-T Rec. P.1202 series and ITU-T Rec. J.343.1. The core module estimating coding quality of each model is described with key algorithms and parametric formulas. The review of each model is presented and the strengths and weakness of each model are remarked. Finally, future work towards the development of an updated parametric QoE model for latest HEVC/H.265 is discussed.