The n-color box-ball system (BBS) is an integrable cellular automaton in one dimension. In the first part, I review its basic features including solitons, ultradiscretization, Yang-Baxter relation, and quantum group symmetry, etc. In the second part, I introduce a randomized version of the BBS and present a recent result on the limit shape of soliton distributions based on thermodynamic Bethe ansatz.