Raqqa, Syria is considered the capital of the Islamic State of Iraq and Syria. ISIS is an extremist group that calls itself the Muslim Caliphate and that controls portions of Iraq and Syria. The Muslim Caliphate is a religiously run state that has existed in different forms throughout history.
The Ottoman Empire was the last officially recognized Muslim Caliphate with Istanbul as the capital. Since the Ottoman Empire dissolved and Turkey was created, there has not been an officially recognized caliphate as of 2014. ISIS and the Muslim Brotherhood located in Egypt are considered extremist and terrorist groups not recognized as official organizations by major countries.