This affects both PC and console and may not affect everyone equally. Battlenet launcher also has a note about it:
We are aware of an issue that is affecting our authentication servers, which may result in slow or failed login attempts. We are currently investigating the cause and will provide updates as they are available.
So don’t panic and be patient till its fixed!
Update: Reports of possible DDoS attack on the servers as the cause, but this is unverified.