Interesting to see the details around how overdrafts work. One part I wasn’t clear on, however:
There are a few cases where your account might still go overdrawn without you expecting it — most notably with delayed transactions from organisations like TfL or bills from hotels that come in late that we can’t reject (because they’re presentments — more detail here). Most of the time, these payments should fall within your £20 buffer, but if they don’t, we’ll notify you through the app and give you at least until midnight of that day to clear it. If you don’t clear it, we’ll just treat the it like the normal overdraft and you’ll be charged 50p/day. This will also be reported to credit reference agencies.
It’s not clear to me what happens to people who don’t have an overdraft on their Monzo account. Would they also be charged and reported to the credit reference agencies, or is there some other consequence (e.g. card being frozen until debt paid off)? It seems like there is a risk of accidentally having an overdraft added to the account (and reported), especially if travelling with sporadic access to data for notifications and the chance to fix any issues.
In the future, it’ll be as easy as tapping the “Overdraft” button on the Card screen, but for now it might take a bit longer so please be patient.
Another reason why I think the Card tab should be renamed. 
This isn’t card specific, it’s about the account. In theory, you could never use the card and still want/use and overdraft.
Thanks for the post, great to see long-discussed features coming to fruition!