Private DayZ servers can now be monetised, which means you can - among other things - limit access to people who pay. In order to be able to monetise your server it must be approved by Bohemia, and those that are will be added to a publicly available list.
If approved you can, as mentioned, charge people to access your server, charge for in-game advertising, and theoretically charge for cosmetic items - the stipulation being that sold items must not affect gameplay. Paying to win, in any form, is forbidden. Approved and monetised servers will be monitored and if they're exploiting people will be removed, and possibly face legal action. There's a FAQ with the nitty-gritty.
Bohemia allowed ArmA 3 servers to be monetised from 1st Feb this year and, as with Arma 3, DayZ server monetisation is considered "a test run". Permission to monetise is temporary and will expire, in DayZ's case, 31st May 2016 (Arma 3 permission expires January 2016). "At that point," said Bohemia, "we will evaluate its effects on the community."
Note that these rules do not apply to public hive DayZ servers or the DayZ mod.
DayZ launched into Early Access in December 2013 - two years ago now. It's sold more than 3.2m units. DayZ is due to launch in full mid-next year, with a beta to begin earlier in 2016. PS4 and Xbox One versions are on the cards but no date has been attached to either version. Maybe later next year?