Abstract: Acidization is one of the main stimulation measurements to increase production of carbonate reservoirs. Once acid is injected into the reservoir matrix and fractures through a wellbore, selective chemical reactions are initiated between mineral rocks and acid, resulting in irregular earthworm-like holes, namely "acid wormholes". Many factors influencing the acid-rock reactions cause the diversity of wormholes. In order to break through the limitations of the existing wormhole modeling, this paper teases out the important achievements of both physical and numerical simulations of acid wormholes during the process of the matrix acidizing in recent decades, and demonstrates the latest progresses on the acid wormhole growth patterns and their shape distributions, 3D wormhole reconstruction technique and detailed wormhole characterization; then further summarizes the deficiencies of existing research ideas and methods on wormholes during matrix acidizing; finally presents some suggestions on experimental instruments and methods, mathematical simulation and characterization methods for acid wormholes.