There were two major Islamic threats to Europe -- in the westernmost part of the West, the Iberian Peninsula, there was an Islamic invasion of the petty Visigothic kingdoms in the 8th century AD, which created an Islamic society that lasted until the 15th century. They attempted expansion to the east, into Francia, but were stopped by a combination of fairly effective Frankish defense and other factors such as rebellious emirs (sometimes working in conjunction with the chief rivals of the Umayyad lords of Muslim Iberia, the Franks and the Abbasids), increasing interest in Mediterranean possessions such as Corsica, Sardinia, and Sicily.

Why the reconquista was a success and drove Islam (both as a state power and, more brutally, as a popular religious belief) out of Iberia isn't easy to sum up with one quick statement. In fact, I'm not sure I'd be able to explain it at all, except to give a one-damn-thing-after-another summary of the alliances, betrayals, battles, sieges, and general ebb and flow of the fortunes of the various Christian and Muslim states of Iberia that ultimately lead to the fall of the last Muslim state of Iberia, Granada.

More recently, there was the Ottoman Empire, whose expansion reached a high water mark at the gates of Vienna in the 16th and 17th century. The Ottoman Empire didn't ultimately conquer Western Europe, but it did conquer the Byzantine Empire. Unlike the gains in Iberia, these have not been entirely lost -- Istanbul is, to this day, part of a nation that is predominantly Muslim, even if Turkey did abandon official Islam with the fall of the Ottoman Empire. In addition, Albanian and Bosnian Islam both date from the Ottoman period.

As for Asia -- well, obviously, Islam had a big impact on western Asia. Zoroastrianism was essentially totally displaced by Islam in Iran. Hinduism survived, but many Indians did become Muslim.

Mongolia is an interesting case: the Golden Horde and the Ilkhanate, two of the Mongol Empire's sub-states, both converted to Islam. In the case of the Ilkhanate -- which started off being predominantly Buddhist and Nestorian Christian -- it made sense as a way of ameliorating relations with predominantly Muslim subjects. The case of the Golden Horde is actually unclear to me -- I don't believe the territories of the Golden Horde were very predominantly Muslim (compared to alternatives like Orthodox Christianity or traditional Tengriism) -- but they did. The Mongolian heartland, however, ultimately became Buddhist.

As for China, Islam did make some headway in China. The two largest groups of Chinese Muslims are the Uyghers and Hui. Uyghers are a Turkic people, predominantly in the west. Hui are basically the same ethnicity as Han Chinese, except for the fact that their ancestors converted to Islam. Most Chinese didn't become Muslim, though.

Tl;dr: Muslims conquered and/or converted a lot of the world, but there's also a lot of the world that they didn't conquer/convert. They didn't convert the whole world to their one universal faith, but then again, no other religion has either.

Maklodes gives a good answer, but met me ask this from OP

Islam had several golden ages of learning, art, science, writings, and more.

How is this related - is learning, art and science supposed to give such a big advantage in military technology that they should be able to conquer Europe? It did not quite work like that back then. Yes, Ottomans used gunpowder earlier than Europeans (borrowed from Asia), yes, Damascus steel was great, but overally you don't see any truly overwhelming advantage in mil-tech at no timepoint.

Or do you mean that this art and science should have been so attractive that it draws peaceful conversions? Medieval Europe did not quite work that way, the Church had a fairly firm grip, crusades were launched against heretics like the Albigensian crusades, this just doesn't work that way that the average Jean in Paris converts to Islam just because Al-Khawarizmi was really smart (even if he would have heard about him at all) and expect that everybody is OK with it. Besides, Europe's first contact with Islam was that they came, they conquered the Iberian peninsula and were stopped only in later France at Tours, meanwhile Muslim pirates ravaged the Mediterrean coastline. It is sort of hard to build up trust and good relations after that. Add the Crusades, add the Ottoman conquests, and basically you will find that the Muslims were often seen as The Enemy (there were some exceptions, some Hispanian Christians were OK with living under Muslim overlords etc. French kings allying with Ottomans etc.).