In this paper we apply a simple representation of Sturmian strings, which we call a “reduction sequence”, to three algorithms. The first algorithm accepts as input a given finite string x and determines in time O(x) whether or not x is Sturmian. The second algorithm is a modification of the first that, in the case that x is Sturmian, outputs a reduction sequence for a superstring u of x that is a prefix of an infinite Sturmian string. The third algorithm uses the reduction sequence of u to compute all the repetitions in u in time Θ(u), thus extending a recent result for Fibonacci strings. The third algorithm is also based on a characterization of the repetitions in a Sturmian string that describes them compactly in terms of “runs”. Finally, for every integer r4, we show how to construct an infinite Sturmian string that contains maximal repetitions of exponents 2,3,…,r−1, but none of exponent r.