The sport of curling has a long history over 500 years and, consequently, a variety of information and experiences have been accumulated on the technique, strategy, coaching, and other facets of the sport. However, very few detailed scientific or quantitative investigations have been made, especially on the stone dynamics, such that a fundamental understanding of the dynamics has yet to be achieved. This report summarizes the previous theoretical and experimental studies of stone dynamics and aims at making clear the areas yet to be solved.