Milestones in counting complexity
There has been a series of breakthroughs on Dichotomy Theorems by Professor Jin-Yi Cai https://rjlipton.wordpress.com/2012/01/20/is-it-time-to-declare-victory-in-counting-complexity/
Another dichotomy theorem https://rjlipton.wordpress.com/2014/06/23/counting-edge-colorings-is-hard/

https://rjlipton.wordpress.com/2011/02/14/classifying-papers-on-classifying-problems/

https://rjlipton.wordpress.com/2009/06/09/computing-very-large-sums/