An IET is rational if it translates points by rational amount. In a finite rational IET, all orbits are periodic. In an infinite IETs, this need not be the case. I will discuss some examples of infinite rational IETs in which it can be proved that almost every point is periodic. Further the dynamics on the aperiodic sets can be completely understood. Theory developed to understand these examples points out an interesting class of infinite IETs admitting a renormalization scheme (though it remains to be seen how effective this scheme is for understanding generic IETs). I will be discussing a preprint joint with Kasra Rafi and Anja Randecker, and a work in progress joint with Anna Tao.