Interval translation maps (ITMs) are non-invertible generalizations of interval exchanges (IETs). The dynamics of finite type ITMs is similar to IETs, while infinite type ITMs are known to exhibit new interesting effects. The finiteness conjecture says that the subset of ITMs of finite type is open, dense, and has full Lebesgue measure. In my talk, I will prove the conjecture for the ITMs of three intervals and discuss some open problems.