Abstract: ZI (zero-inflated) data are data with overmuch zeroes. The ZI data have been commonly encountered in a wide variation of disciplines, and have been a hot topic since last decade. In this paper, we first present the actual significance of ZI data via two examples. Then we demonstrate the general situation and latest improvement of statistical analysis for zero-inflated data. Additionally, zero-inflated models, zero-inflated mixed models, and the estimation methods and some diagnostic problems are surveyed systematically. The relevant work done by authors in recent years are also introduced. Finally, several potential topics to be studied are listed.