This talk gives an introduction to my approach to foundation-theoretic epistemology which is based on the method of optimality justifications originally developed in the domain of meta-induction. Optimality justifications attempt to provide a new solution to the problem of the justificational regress. Rather than striving for a priori demonstrations of the reliability of epistemologcial methods, which is impossible, they attempt show that certain epistemic methods are optimal for a given epistemic goal among all accessible alternative methods. The transition from the established optimality of a method to the acceptability of particular beliefs generated by the method is accomplished by so-called optimality principles. In the second half of the talk the method of optimality justifications is carried out for three fundamental problems:  the justification of induction, theory-generating abduction, and logic.