Gelled acid is a common retarded acid system，which is widely used in acidizing and fracturing operations to enhance oil and gas production for carbonate reservoir. The key of gelled acid is the polymer thickening agent，which can impart the acid solution high viscosity and good performances，thus the research of thickener has gained intense attention during the past decades. In this article，we reviewed the research history and recent advances of thickener in this area，and particularly focused on the molecular structure design and preparation of thickener，the performances and practical applications of corresponding gelled acids. Moreover，the advantages and disadvantages of different thickening agents were discussed，and a special attention was given to discuss the strategy that how to optimize the molecular structure of thickener and improve the performances of the gelled acid. Furthermore，we also discussed the challenges that concern the future development of gelled acid.