A substitution rule is an algorithm for replacing a symbol with a finite string of symbols (for example, replace 0 by 01 and replace 1 by 0) and a substitution sequence is a sequence obtained from repeated applications of the substitution rule. A Sturmian sequence is a non-periodic sequence of minimal complexity. Both of these objects that are central to the study of mathematical models of quasicrystals. We will discuss interesting dynamical, algebraic, and combinatorial properties of these two families of sequences, as well as their relation to each other.