I'm not sure if you would call it a "breakthrough" per se, But the Publishing of Probability Theory: The Logic of Science By Edwin Jaynes and Larry Bretthorst may be noteworthy. Some of the things they do here are:
show equivalence between some iterative "seasonal adjustment" schemes and Bayesian "nuisance parameter" integration.
resolved the so called "Marginalisation Paradox" - thought to be the "death of bayesianism" by some, and the "death of improper priors" by others.
the idea that probability describes a state of knowledge about a proposition being true or false, as opposed to describing a physical property of the world.
The first three chapters of this book are available for free [here] 1.