In minimal model program, divisorial contractions, flips and flops are considered to be elementary maps. The seminal works of Kollár and Mori classified threefold extremal neighborhoods and hence leads to the existence of flips. It is tempting to have explicit description of birational maps in minimal model program in dimension three.  In this talk, we are going to present the recent progress on classification of threefold divisorial contraction to curves. First of all, it can be realized as a weighted blowup by considering embedding into higher dimensional ambient space. Under the extra assumption that the image curve is smooth, we have an algorithm which leads to a classification of divisorial contractions. 

This is a joint work with H.K. Chen and J.J. Chen.