Not long after the foundation of Islam and the life of Mohammed, about 650 AD, there were people who became known as Sufis (SOO-fees). Sufis can be Sunni or Shiite. These people wanted a more direct relationship with God. Instead of just doing things like praying or good deeds, or the Hajj to Mecca, Sufis wanted to experience the greatness of God within themselves, through meditation or through ecstatic dancing or in other ways.
Here's a video of some Sufi dancing.
The "whirling dervishes", for example, are a branch of Sufism that got started about 1300 AD in the Seljuk empire, where people used dancing to get themselves into a religious frenzy that helped them have a personal experience of God.
Other Sufis, like al Tusi in the 1200s AD, were more philosophical, looking for ways to use logical thought to get closer to God. In this way they were like the Neo-Platonists of a thousand years earlier.
Another way that Sufis tried to get closer to God was by eating roasted coffee beans, which they got from East African traders. Sufi people were the first people outside of East Africa to use coffee, about 1450 AD.
To find out more about Sufism, check out these books from Amazon or from your local library: