According to Apple's System Status website, the App Store, the Apple TV, Apple Music, and the Mac App Store are currently experiencing service issues.
Many Apple customers have also been complaining of App Store issues on Twitter, Reddit, and other social networks. Affected customers are unable to download apps and in some cases, can't load the App Store at all.
Service interruptions have been ongoing since approximately 4:00 p.m. Pacific Time and there's no word on when service will be fully restored.
The issues could potentially be related to the release of Super Mario Run and the strain that it is causing on the App Store due to its popularity.