Earlier this month, Wizards of the Coast put out optional rules for downtime in 5th Edition (accessible here).
Overall, what I saw was encouraging.
It's good to see WotC thinking in terms of a long-form campaign, and what players are doing between adventures. Specific downtime activities I was happy to see include: rules for crafting items of all kinds (and particularly magic items or spell scrolls), rules for training language or tool proficiencies, rules for research of lore regarding foes or locations, and rules for buying and selling magic items.
It was kinda janky to see activities like criminal heists and pit fighting included among downtime activities. They seem more like mini-adventures in and of themselves, to me. The only way I can think to justify it is to say that they're presented in this compressed, abstract format so that one player doesn't take a lot of time away from the party by going out on a mini-adventure of their own while everyone waits for them to finish - which makes sense, I suppose.
The suggestion regarding "foils" (basically villains by another name?) also seemed really out-of-place, especially given that they were given spatial priority in the document. All it really ended up saying is that "yeah, sometimes opponents of the party will be up to stuff while the players are on downtime, too." (I don't think it should take three full letter-size pages to say that.)
I would've liked to see rules regarding more domain-style play, like creating and running factions or building and maintaining manors/castles/towers and their demesnes. (Perhaps that would be another Unearthed Arcana in and of itself, though - which I would be cool with.)
I'm currently running a (heavily-hacked) 5E game, and these rules are fairly lightweight and easy to bolt on without much meddling - and my campaign utilizes downtime. I think I will take advantage of these.