  The program Reverse Mathematics in the foundations of mathematics seeks to
identify the minimal axioms required to prove theorems of ordinary mathematics.
One always assumes the base theory, a logical system embodying computable
mathematics. As it turns out, many (most?) theorems are either provable in said
base theory, or equivalent to one of four logical systems, collectively called
the Big Five. This paper provides an overview of two recent extensions of the
Big Five, working in Kohlenbach's higher-order framework. On one hand, we
obtain a large number of equivalences between the second-order Big Five and
third-order theorems of real analysis dealing with possibly discontinuous
functions. On the other hand, we identify four new 'Big' systems, i.e. boasting
many equivalences over the base theory, namely the uncountability of the reals,
the Jordan decomposition theorem, the Baire category theorem, and Tao's pigeon
hole principle for the Lebesgue measure. We discuss a connection to
hyperarithmetical analysis, completing the picture.
