What are some exciting non-STEM breakthroughs happening now?

"Breakthrough" is a tough word here...

How about the TurDuckEn? https://en.wikipedia.org/wiki/Turducken Or the Pake (PieCaken, Cherpumple, or whatever you call a pie baked into a cake).

I'm at least half serious -- the arts, including culinary arts, is a place to look. The color indigo comes to mind as an older example (even if science discovered it, it was a breakthrough due to its adoption in art and fashion)... lately Black 3.0 (or Vantablack) may have made enough ripples to count.

Have there been Legal or Political breakthroughs? Was reopening the Cuban border a "breakthrough"? Is electing female world leaders a "breakthrough"? Legalizing gay marriage? Marijuana decriminalization? I could make an argument for any of those.

I'd make a list of what you think "non-stem" areas are (by career, maybe) and look into that. Finance, real-estate, mechanics, art, fashion -- they probably have "breakthroughs" that people outside the fields are not familiar with, at various scales.

One random breakthrough in political science I happen to know about is Experimental(ist) governance.

The common way of thinking about a legislature is that it enacts laws that are just. That which is in the eyes of the population "bad" is outlawed and what is "good" is kept legal. That's a model that has been with us since antiquity. Of course, in the old days the law came from the God(s) but the point was the same -- differentiate between right and wrong.

Experimental governance brings in a completely new way of thinking (+). The legislature is instead seen as an experimenter and laws are seen as tools to use to regulate the behavior of the populace. Maybe the government identifies X as a problem, so a temporary law A to combat the problem is drafted. The law is enacted but with a provision so that it expires after say an evaluation period of 18 months. Then the government studies what effects the law had. If the negatives outweighs the positives, maybe try law B instead and the process repeats itself.

The advantages to experimental governance is that laws can be enacted quickly and in response to changing circumstances. And that "beta testing" makes it easier to write tighter laws free of loop-holes and other problems. Disadvantages include: 1) Regimes can abuse the system by extending quickly drafted temporary laws indefinitely (e.g Patriot Act). 2) If there are no checks and balances built into the system, arbitrary or contradictory laws can be enacted. 3) If the population isn't following the political debate, it might not be aware of what the law is. Thus, EG works best in stable democracies with educated populations, like the EU countries where it is used extensively.

+ Of course no idea is 100 % new, but I know of no similar historical precedent. Temporary laws and decrees have been used in the past, but afaik they have always been considered aberrations and not "natural parts of the system."

This is a very naive question, but can someone give an example of a breakthrough in non-STEM fields? Because now that I've been thinking about possible examples, maybe psychology etc., all fields are inherently a form of science, right?

A lot of people are getting jacked.

There are some breakout genres of self-published entertainment, using Amazon self-publishing for novels, or using YouTube.

Golf course design the past few decades seems to have gotten out of a rut.

I don't know if this is a breakthrough in the sense you're looking for, but one needs only to look at China to see how much better company management has improved. Of course they have their problems and you could argue that they're just copying the western model to a certain degree, but if that was so easy why isn't everyone else achieving the kind of growth China is?

I think there is quite a bit going on now in cognitive psychology as it pertains to education of children. I hear more and more references to mindset and grit.

Biggest political and governance breakthrough that will happen in my lifetime most likely is the boomers dying off. There will be no continuity of their policies which the rest of us have come of age with and generally abhor. 15 years to go, and the decline is already happening.