RFERL has an infographics map of who is helping fight the Islamic State, and what they are actually doing, or not doing, as the case may be.
Naturally, the U.S. is taking the lead- because no-one else will- with strong support from the U.K., France, and a few other countries, to a lesser degree. But the United States is the only nation launching air strikes in both Syria and Iraq.
Some are targeting just Iraq, some just Syria, others are providing weapons, some humanitarian aid, and some just words of support. One would think that since ISIS is practically in their back yard, and the Ottoman Empire and the Gates Of Vienna occurred in the not so distant past, European nations would be more active in attempts to eradicate ISIS, but no.
There are supposedly 62 partners in the coalition, including the EU and the Arab League.
You can view it here.