Twitter Status, check
Whether you are alone with the Problem stand, you can click on the Twitter Status page to check. But note, before Twitter informs on the Status page of something, it can take half an hour to an hour.
Twitter down: check Status
Despite the Downtime on Tweets access
You can try the Twitter App for Android and iOS access to Twitter. If you get also no access to Twitter, then just wait for help unfortunately. However, one thing is usually possible If you just don't want to tweet, you can search through Google for a Tweet and to access the Cache.
If you are in front of Twitter-down phases of fear, you can at least your own Tweets offline as a Twitter archive download.
