Comparing Two Algorithms for 3SUM problem over Integers
The first paper essentially gives a subquadratic algorithm if we know that every input number has $w$ bits and we can add two $w$ bit numbers in one step. This was not a very surprising result and it did not rule out an $\Omega(n^2)$ bound.

The second paper does not use any such assumptions and improves the exponent of $n$ for decision trees, which is a surprise, although not as big as it would be for all algorithms, for which they have only improved slightly (thus disproving the strongest conjecture). I would guess that more results will follow shortly.