Apple's System Status site indicate that several services were down Thursday afternoon. As of this writing, affected services include the App Store, some, though not all iCloud services, the Mac App Store, iTunes in the Cloud, Apple TV, Photos, Mail Drop, and iWork for iCloud.
Apple issued the following two specific notes on the outage:
Multiple iCloud Services - Some users are affected
Users are experiencing a problem with the service listed above. We are investigating and will update the status as more information becomes available.
Multiple Store Services - Some users are affected
Users are experiencing a problem with the service listed above. We are investigating and will update the status as more information becomes available.
These outages seldom last for long, but the screenshot below offers a snapshot for those wanting to track progress on the live page.
Apple Systems Status on June 2nd, 2016
(Tap the image for a larger version)