Microsoft has lowered the status of Xbox LIVE from Defcon 5 to Defcon 3. That is, the Xbox LIVE core services are "up and running" on Xbox One and Xbox 360, though some apps are "limited". (Quick side note: I don't think Microsoft actually uses Defcon; I just like how it sounds).
Anyway, the core services are back up, so you should be able to access your Xbox LIVE account and play games online with no problem. However, Microsoft notes two apps in particular — PBS and Twitch — are "limited" on both Xbox One and Xbox 360. The good news is that they are aware of the issue and working alongside the partners to resolve the issue.
Here is the current status for both:
PBS
"Can’t find the PBS application, Xbox members? We’re aware of this issue, and we're working alongside our partner to get this resolved as fast as we can. We appreciate your patience in the meantime, and we’ll update you as soon as we have more information."
Twitch
"Having trouble trying to play certain content from the Twitch application? We’re working closely with our partner to resolve this issue ASAP. Thanks for staying patient, Xbox members. We’ll keep you posted when we have more information."
