Subhash Khot, Dor Minzer and Muli Safra's 2018 work "Pseudorandom Sets in Grassmann Graph have Near-Perfect Expansion" has gotten us ["half way"][1] to the Unique Games Conjecture and is methodologically quite interesting according to people more knowledgeable than I. Quoting Boaz Barak,

This establishes for the first time hardness of unique games in the regime for which a sub-exponential time algorithm was known, and hence (necessarily) uses a reduction with some (large) polynomial blowup. While it is theoretically still possible for the unique games conjecture to be false (as I personally believed would be the case until this latest sequence of results) the most likely scenario is now that the UGC is true, and the complexity of the UG(s,c) problem looks something like the following...

The paper has caused some researchers (including Barak) to publicly change their opinion on the truth of the UGC (from false to true).

Subhash Khot, Dor Minzer and Muli Safra's 2018 work "Pseudorandom Sets in Grassmann Graph have Near-Perfect Expansion" has gotten us "half way" to the Unique Games Conjecture and is methodologically quite interesting according to people more knowledgeable than I. Quoting Boaz Barak,

This establishes for the first time hardness of unique games in the regime for which a sub-exponential time algorithm was known, and hence (necessarily) uses a reduction with some (large) polynomial blowup. While it is theoretically still possible for the unique games conjecture to be false (as I personally believed would be the case until this latest sequence of results) the most likely scenario is now that the UGC is true, and the complexity of the UG(s,c) problem looks something like the following...

The paper has caused some researchers (including Barak) to publicly change their opinion on the truth of the UGC (from false to true).