Update 2: It looks like Epic will be able to fix the issues with Fortnite Battle Royale's game modes (you can't currently play duos or squads with friends) without taking the game offline after all. You might have connection problems, though.
We think we’ve found a fix for these social/friend issues that does not require downtime. Players may have connection/matchmaking issues as we deploy, if this occurs continue to retry. We’ll update again once we’ve started.January 27, 2018
Update 1: Fortnite Battle Royale players are currently unable to jump into the game with friends. Epic initially said it'd have to take the game offline later today (see below) to fix the problem, but now it says that might not be necessary.
Party/Social services are continuing to be impacted. We're investigating ways to mitigate & are continuing to look for the cause. We're unsure if downtime will be necessary today.January 27, 2018
I'll keep an eye out for any more updates, and it's probably worth checking the Fortnite Twitter page before you jump into a game, too.
Fortnite Battle Royale emerged from 14 hours of downtime yesterday carrying a chest full of bugs, and despite a hasty patch the game is still pretty shaky. The latest issue is that you can't currently play with friends: you can only join a solo game or play with random players in a duo or squad. Epic plans to take the game offline later today to fix that.
The Fortnite party service is down, and Solo and Fill are the only modes available. Players should expect downtime to fix the problem later today.January 27, 2018
This week's problems are all down to a big spike in player numbers, Epic said on Reddit. "We were not prepared for it. We have had a ton of issues and we are working hard to getting them sorted. We can't apologize to our players enough, and you can be sure that we are going to make this right. We can only ask you for your patience."
And, at the moment, the community does seem to have a fair bit of patience. Judging by the reaction I've read (mainly on Reddit), people are happy to wait for Epic to resolve the problems. But let's hope that today's downtime doesn't last as long as yesterday's, and that the next inevitable bump in player numbers doesn't cause similar issues.
When the game goes offline later (Epic has not yet specified a time), read our guide to the best drop locations in the game. That way, your first round back will be a good one.