If you're experiencing issues with iMessage today, you're not alone. According to Apple's system status page, the service is "not working as expected for some users." As for specifics, Apple says the following:
When sending a message to someone running iOS 8 or earlier, the message may not show as delivered, even when the message has been delivered.
So, it sounds as if messages are still going through, but you may not be able to tell whether they were delivered or not if the person you're messaging is running iOS 8 or earlier. According to Apple's timeline, it looks like the issue has been persistent for most of the day, but it'll hopefully be cleared up soon.