Snow and ice animation methods are becoming increasingly popular in the field of computer graphics (CG). The applications of snow and ice in CG are varied, ranging from generating realistic background landscapes to avalanches and physical interaction with objects in movies, games, etc. Over the past two decades, several methods have been proposed to capture the time-evolving physical appearance or simulation of snow and ice using different models at different scales. This state-of-the-art report aims to identify existing animation methods in the field, provide an up-to-date summary of the research in CG, and identify gaps for promising future work. Furthermore, we also attempt to identify the primarily related work done on snow and ice in some other disciplines, such as civil or mechanical engineering, and draw a parallel with the similarities and differences in CG.