This is a complicated question, not the least because many things can happen that we don't expect. No one in the 1800s could have expected the world today!

Islam in today's world is heavily interwoven with the social and political challenges and changes of the past century, especially regarding Westernization, the framework of modernity (secularism, the nation-state system, etc), and changes in technology. For instance, "Islam" and "the West" are often treated as antonyms.

In the coming centuries, I think that (a) the power center of the world will shift away from Western countries, probably to somewhere in Asia; therefore, "Islam and the West" will no longer be a defining issue. Often, today, identity is a heavy part of Islamic discourse (for instance, hijab as the "flag of Islam"), and I think this will lessen as cultural and economic power shifts to other regions.

Also, in the past century, many Muslims have reframed their approach to Islam in light of paradigms that are part of modernity (such as science as a modern-day replacement for religion, promoting political systems such as communism or democracy, technology as the savior, Islam as "modern", the worship of progress). The world is starting to see that modernity (technologcal or ideological) isn't the savior that it was once thought to be and has in fact brought a lot of harm and suffering along with good, but I feel that sometimes Islamic discourse is a bit slow to move on from these things. In fact some Muslims are still citing Victorian-era authors to "prove" Islam. I think that Muslims will eventually move on with this as the rest of the world is, but it might take a little more time. 

Some of the social changes that came with technology, especially regarding gender roles or the democratization of knowledge, have been uncomfortable and contentious; and often, there is a conflict between having a traditional paradigm in mind and the real-life lives that we live. I think this will sort itself out and Islamic thought will adapt to the new realities we are living in. 

That being said, I suspect that many things that have been "traditional" over the in various places will continue to be so. Things become "traditional" because they are functional (even if not ideal) and in some places there will not be a big change. 

Also, (b) I think that environmental concerns will become a top priority, and the need for basics such as drinkable water and clean air will overshadow many of the issues that are considered important today.

I HOPE that there will be a reduction of poverty and warfare in Muslim-majority countries and improvements in political justice. (This is not to say that every Muslim-majority country is dimsal but we are aware these are problems in much of the Muslim-majority world.) Really the political situation seemed to hit an all time low in the 20th century so one hopes it can't get much worse. 

Regarding Islamic thought, I expect that there will be a widening gap between (a) literal/traditional interpretations of Islam (for instance, literal derivations of fiqh) and (b) "reformist" views which promote things such as deriving law from the spirit of the text, rather than the actual text, or focus on social contextualization. 

There are just a couple thoughts, and I am sure others will have thoughts as well!