The above screen is what I get as I logged in to Twitter, today. So, I checked with others and here is what they have to say –
Twitter problems are occurring on a large range of devices as there is an ability to tweet from game consoles, televisions, mobile phones, tablets, personal computer and other gadgets that auto tweet. 
The above image is the Twitter server status page which informs you that the service is down.
According to a new source- Twitter confirmed the status of  the outage at 9.00GMT. It also stated “Some users are currently experiencing problems accessing Twitter. We are aware of the issue and are working towards a resolution.”

Hope, it is up soon. You can check this link for outage related issue.
Are you having Twitter problems? Do share your experience.