In this short note, it is shown that the (regular) Sturm-Liouville operator has a Riesz basis of eigenvectors and that the spectrum is totally disconnected, i.e.one cannot go from one spectral point to another without leaving the spectral set. This brings them in the class of Riesz-spectral operators introduced in the book by R. Curtain and H. Zwart [An introduction to infinite-dimensional linear systems theory (1995; Zbl 0839.93001)]. For this class many system-theoretic properties are easily characterized. As is said by the authors, the results are known but scattered in the literature, and one may regard this article as a short overview article on Sturm-Liouville operators.