This article needs contribution. Mongol Invasion is a very important event later in the game and should be covered for players who have not experienced it.
Sounds Like a Nice Man.
In January of the year 1215, you will get a rather ominous message telling you of rumours of a Khan of Khans in the east. This is the game's way of telling you that everything you know and love about your insignificant kingdom/empire/duchy will be utterly destroyed, or, more formally, that the Mongols are about to arrive on the scene. All will be quiet, however, until May of 1218, at which time you will receive a second message telling you that the Scourge has arrived, and if you examine the Khan's character page, which is accessible from his portrait in the message, you will see that he has invaded Persia (as historically happened when the Persians dismissed the Khan's diplomats, rather against their better judgement). For now, the Europeans are safe; the Hordes are not coming your way just yet. The Ilkhanate will then come bearing at least 121 thousand troops to invade Persia and will usually be successful with that. Usually with the original version you will get those 121 thousand troops, however, with the new patches, you won't get those courtiers and troops any longer. The Ilkhanate will attempt to invade many Muslim (and non-Muslim) nations across the Middle East and will usually succeed, starting with Khiva and it will keep going to Mesopotamia (and, in some cases, the Mediterranean coast). Unfortunately, the Ilkhanate doesn't conquer alone...
The Golden Horde
If you start a new single player game in 1337, you will see not one, but two Mongol hordes on the map. Yes, this means another devastating horde is coming Europe's way. While the Ilkhanate's targets are Muslim, and mainly in the Middle East, you will get another message about the second scourge coming Europe's way. This other horde, the Golden Horde, is here to conquer Europe all the way west to the Atlantic (or so the message says)! Europe's fate depends on the ability of its lords to band together and fight off the Horde! This horde will bear 100k troops to conquer first Cumania and then the Russian duchies (or perhaps a unified Russian kingdom) if you let it happen, and they will do it with incredible ease. If you let them get that far, they will conquer a large portion of Eastern Europe and will generally launch a few invasions here and there, but with their large amount of land and the likely rebellions within their borders, most of Europe can breathe easily for a while. You have to be careful however, because of the final horde that will arrive in only a few short decades...
Timur and the Last Horde
By the late 1290s or early 1310s, the Hordes will usually stop expanding for good, and they will usually face a large amount of rebelling vassals. On the other hand, another horde will be coming, denying any respite from the previous two. From Transoxania in the East, Timur (aka Tamerlame) will emerge, an ambitious khan with dreams of restoring the Mongol Empire first forged by Genghis Khan. In the 1360s or 1370s you will receive another message about one last final horde coming called the Timurids. They will arrive in the Easter Ilkhanate, around Khiva. Unlike the previous two hordes, they will start with the Shia religion and will start their conquest on the Ilkhanate or Khiva depending on Khiva's state as a nation. In any case, the Timurids will almost always conquer most of the Ilkhanate, but can be stopped by rebelling vassals. After the three hordes, nothing more will come from the steppes.
How to Fight Back the Mongols
If you want to fight the Mongols back to whence they came from, then there are several things you should be thinking about before you even consider pressing the Space button and facing the Grim Reaper incarnate. First, you must know how to please your vassals and allies before you even take on these fates; two, you must have a LOT of cash; three, you armies must number at least 120k combined, THAT IS A MINIMUM; four, you must have basic knowledge of probabilities. The first three can be understandable, and although the last one might not make sense, it is also important.
To please your vassals, you must give them what they want as in de jure vassals or de jure counties that you hold that belongs to your vassal's duchy. Then, bribe them off by sending gifts that will increase their opinion of you and therefore giving you more levies. To please your allies, you can send them gifts again, although it might be a drain in your pocket, this move can be useful in the end. With this, you can have a large enough levy to fight the Mongols off and your allies are more willing to help your pitiful nation.
To fight them off, you must have a LOT of cash, why? To feed up and upkeep your armies and retinues. Your vassals' force of levies are the most important backbone of the army, and you must please them enough by sending in constant cash to them to make sure they can pay for their upkeep since it's their troops. Your retinues are another problem. If you have updated to the most recent patch and have the Legacy of Rome DLC then you can issue out retinues. Using retinues can balance off levies because they recover fast and they are easy to manage, but takes a lot of cash to manage their upkeep. So, the most reasonable amount to have is at least 10k gold, more is better. If you win, then you can get a lot of cash to pay for the reparations to your vassals.
Your army is the most important thing that is needed to fight the Mongols off. Since your enemy has 141.4k troops at least, not counting levies, your armies must be at least 100k strong, AT LEAST. Combining your levies and retinues can give you a estimated value enough to compare the amount of troops. If you have 120k and you have lots of allies willing to help you and bolster another 75k, then you are safe to fight them off. The commanders are also important, since you will need a martial of 15 minimum to give out an advantage. Then what you need is to find counties that will give you the natural advantage while giving the Mongols a disadvantage. A county with a stream or a mountain can be useful to you.
The probabilities are possibly the most absurd, but nevertheless also important part of facing the Mongols. If you are a Western European nation like France, HRE or England, than this is practically useless because it's an impossible probability to fight them because due to their large size, they will have rebelling vassals that will hinder their progress. But if you are a Persian Sultanate, A Russian Kingdom/Duchy, then this will apply to you. Consider this: if the Sultanate of Khiva is taken and there are two possible nations to invade, yours or Cumania, which one will the Ilkhanate choose? It's always a 50:50 shot, if you are not invaded then use whatever time you have to continue to build up while trying to evade the inevitable or if you are invaded, use up whatever idea you have in mind and beat them off. Another possibility is this: You are a Russian duke/king, you have the largest army amongst any other Russians. Then the Golden Horde arrives, and takes Cumania. Which of the duchies is next? If you are one amongst 16 others then the chance is 1/16 you will be invaded. But they will consider who has the largest army and will try to invade that person before they become a threat, if you are THAT person, congratulations, your ass is going to get handed back to you in less than an in-game year if you don't plan ahead.
In all, it's all about planning, Get it right, you can fight back. Get it wrong, then congrats, your ass is going to be hanged in a Mongolian yurt.