Abstract:  In this talk I will give an over-view of the Stieltjes integral and  review some of the many definitions that appear in the literature.  I will talk about the strengths and weaknesses of each, particularly in relationship to the classical Darboux and Riemann integrals.  I will conclude with a discussion of a new definition which I believe is better than the previous definitions.  This is partly based on joint work with my former undergraduate student, Greg Convertito.