We will discuss interval exchange transformations (IETs). These dynamical systems arose as a natural generalization of rotations on the unit circle and were shown to be directly related to flows on translation surfaces. These systems may be naturally expressed as symbolic dynamical systems (i.e. shifts) with specific properties. We will discuss this relationship and consider problems for IETs and their analogues for shifts. In particular, we will examine self-similar IETs which may be expressed by substitution shifts.