It's been a tough few months of connection and lag issues for Blizzard. If you're trying to login to their Battle.Net service to play any game they have on offer, it might be worth giving it a few hours.
As confirmed on their Customer Service Twitter account, Blizzard's login servers are experiencing connection issues and are developing long queues for users. Even more unfortunate for them was commenting on a time they expect the servers to be operational - four hours ago they stated a 90-minute wait, followed by a Tweet two hours ago claiming only 60 minutes until the servers are operational.
As you can see, their latest Tweets simply tells everyone to stay posted for updates, here's hoping they will be fixed soon.
As Heroes of the Storm is in the full swing of development, this marks three eSports related games that Blizzard have on offer. If you're a professional gamer and make your living by playing, streaming or competing in tournaments for StarCraft II, Hearthstone or Heroes of the Storm, I cannot imagine you would be very happy at these continued connection issues.
We will continue to report as the story progresses.