I think you are talking about the ductless wall units. They’ve been around quite a while, but I have noticed them gaining popularity recently.
I have a pair of them. There are quite a few advantages: It is almost completely silent since (like central AC) the compressor is outdoors away from the windows, unlike noisy window AC units. A relatively small indoor unit cools a very large area, since (almost) everything depends on the size of the outdoor compressor. It does not block up a window. Leaving it installed over the winter will not create a freezing draft. Compared to central, it is a lot cheaper to install because there is no need for duct work, and it is a better option if you don’t want to give up space for installing ducts for the same reason.
It is also quite a bit more energy efficient than a window unit, with the EER running in the area of 14 as compared to window units that max out at around 10 or 11. (EER is the ratio of BTU over wattage, e.g. a 10,000 BTU that draws 1,000 watts has an EER of 10. You can find this information on the side sticker).
Disadvantages that I am aware of are 1) the cost of purchase and installation, which is more than buying a number of individual window units and 2) I find that they do not operate as effectively when turned on and off – it works best when left on thermostat 24/7. This makes operation more costly than window units which I was accustomed to turning off when not using the room.
Overall I give them thumbs up. If you have any other questions I will try to answer them.