Their primary weakness was that they were almost entirely reliant upon cavalry. Mongol tactics, training and organization were focused on mounted combat, and although they could be flexible -- for example, by using Chinese and other engineers for help with breaching defenses when it came to siege warfare (which required infantry units as well) -- they were inevitably hampered by more mountainous, broken terrain compared to their success in the open Steppes.
The army was almost entirely composed of cavalry, with forty percent heavy cavalry, and the remaining sixty percent designated light cavalry. There were no organic Mongol infantry units, but often units of conquered peoples (or even their civilian populations) were pressed into service for specific campaigns. These units were considered entirely expendable. It was common Mongol practice to attack the outlying and less defended cities and towns before bringing a major city or fortress under attack. The captured populations of these towns were then driven forward in advance of the Mongol army and forced directly against the enemy army. Often these "infantry" were used as laborers in sieges, or driven against the walls of a city where they suffered terrible casualties...." Genghis Khan's Greatest General: Subotai the Valiant by Richard A. Gabriel
Common Mongol cavalry tactics -- for example, the devastating hit-and-run tactic of circling with light cavalry and chipping away at enemy formations with flights of arrows, then retreating swiftly -- don't adapt well to infantry combat. In addition, the ability to cover great distances so as to take an enemy by surprise is hampered to a degree by the mountainous (and forested) terrain of Europe and the Caucasus.
Not that these problems couldn't be overcome: Mongol forces easily won most of their major engagements with Europeans. But the terrain wasn't a natural fit for their most successful tactics.
Massive cavalry armies also have a serious logistical problem. A Mongolian "tuman," the largest military division, consisted of 10,000 mounted soldiers, each of whom traveled with and often fought with 3-4 spare mounts. 40,000 horses require a lot of forage, and overgrazing was a continual issue.
The Mongols were weakest on uneven terrain. Early in the history of the Empire, expansion occurred on the Eurasian steppe. Conquest of the Xi-Xia dynasty (the Tanguts) and the campaign against the Jin state (the Jurchens) [1209-1211] occurred on the steppe in north China. Conquest of the Kara-Khitani (1218) took place on steppe. The Khwarezmian sultante (taken between 1219-1221) occupied more varied territory but had vast expanses of plain and shrub-land.
It's worth noting that the Jin dynasty was not conquered until the 1230s, after the death of Chinggis. For the southern portions of the Jin dynasty and the later conquest of the Song, the Mongols were campaigning in the most densely populated regions on earth. These areas were divided into agricultural tracts that were often difficult for the cavalry maneuvers that the Mongols were so dependent on. Especially during the reign of Kublai, the Mongols developed infantry tactics to counter Chinese forces. Heavy infantry were also utilized in later campaigns against the Vietnamese kingdom and Indonesian states.
Their cavalry warfare was apparently more flexible than one might think, given the success of their attacks on Georgia and their travel through the Caucasus mountains in the 1220s. The Mongols later returned and conquered Georgia, though I don't much about their tactics in those campaigns as well as their conquest of Afghanistan.
The obliteration of the Russian principalities during the reign of Ogedei by Batu again show the Mongols in their favorite steppe landscape.
In 1241, Batu engages the King of Hungary, Bela IV, at the Battle of Mohacs. The King is reinforced, barely, by troops from the Holy Roman Empire as well as militant monastic orders (perhaps even the Teutonic Knights). As the infantry and heavy cav are overwhelmed by Mongol maneuvering and constant missile fire, the European forces collapse. Bela IV flees south, and the Mongols pursue him, sacking city after city.
After Mohacs, the Mongols took over Hungary, killing between 1/2-2/3 of the entire population. However, they stopped where the Eurasian steppe met the mixed-forest terrain of Eastern Europe. The death of Ogedei prevented Batu from raiding further, but it can only be speculated as to what was the more pressing deterrent- the need for Batu to return to the capital, or the dense forest that would have made cavalry maneuvers difficult. It has also been speculated that the Mongols were unimpressed by eastern European material culture after already having conquered the Middle East and China. (I don't know if I buy that though). The Mongols would return mid-century to raid Poland and parts of the Balkans, including Byzantine Thrace.
Although the Mongols were able to modify their infantry tactics to take all of China, that conquest was extremely protracted (1235-1279). The Mongols did not take east Europe far beyond the steppe, and it's very likely that geography was the deciding factor for that.
Also- it's worth noting that in the first real Mongol defeat- Ain Jalut in 1260- Baibars of Egypt was able to lure Mongol forces into a forested highland ridge. Surrounded head on and flanked by infantry, the Mongols were unable to maneuver and were finished off by a rear Mameluke cavalry assault. ( An animated power point of the battle can be found here ).
Sources- The Mongols and Global History by Morris Rossabi, also The Mongols: A Very Short Introduction
Short answer to your question? Yes. A slightly more detailed answer follows below.
The Mongols were on par with the Republican Romans when it came to fighting and defeating their contemporaries, some of the systemic / strategic advantages the Mongols had (mobility I would club as a tactical advantage) was fairly similar to the Roman edge and this contributed to their success.
STRATEGIC / BIGGER PICTURE ADVANTAGE (in no particular order)
Meritocratic system that promoted and ensured only the best generals rose to the top. This then percolated down to the line as well. In my opinion (if you study their campaigns) a Jebe or a Subutai (Generals of Chenghiz) are by themselves world class generals I would personally rate amongst the finest in history, and they got their position by virtue of their skill and not because they curried favour with the Khan. A supremely capable leadership meant they were empowered and capable of acting independently.
None of the disadvantages of operating under either a feudal setup or a settled society - Contrary to what Hollywood might have us believe, most European (China was a different matter) armies were feudal in nature and were hardly standing armies of professionals , they were instead comprised vastly of peasants operating under a core of professional soldiers we would call knights. This had it's own set of issues, discipline, coherence were big ones (I would address these in the tactical area) but it also meant that campaigning seasons were largely determined by the harvest periods. Extended campaigning would mean lesser manpower to harvest the fields and this was not a tenable situation. The Mongols however, by virute of being pastoral nomads could even campaign for a half a decade or longer, they had no roots to tie them down, no harvests to attend to and this gave the Khans immense flexibility while organising campaigns.
Army organisation (this goes along with the next point) - Chengiz organised his army on a decimal system - Tumen=10,000 soldiers, Minghun=1,000, Jagun=100 & Arban = 10. What this did was it gave the Khan and his top generals supreme flexibility and adaptability in organising campaigns which when clubbed with...
Principle of Auftragstaktik both at a tactical as well as a strategic level, and this again gave the Khans immense strength and flexibility. For instance the raid into Georgia & Armenia by Subetai was based on a simple reconnaisance mission that Genghis assigned Subetai. How it was executed, the targets, the objectives etc were left for Subetai to decide.
All these three advantages the Romans also very broadly enjoyed.
TACTICAL ADVANTAGES
The second advantage these hardy ponies conferred on the Mongolians was the ability to campaign even in winter, something which other Medieval armies were hard pressed to do. The Mongols for instance, invaded Russia (what we know as Russia today) at the start of the winter! A season when campaigning was not done usually if at all.
MISCELLANEOUS
Aside from these, you had the points other forum patrons have already raised. The Recurved Composite Bow, Advanced cavalry tactics such as the feigned retreat.
Sources :
You want a starting point (though I personally found a few inconsistencies based on the other sources I have read), Dan Carlin's Wrath of the Khans podcast is very good, and you can kick off your own research after using that as a jumping point (or as I did, read stuff and then listen to it)
The Mongols were a dominant military force in many of the theaters in which they fought. If you look at where most of their key victories in Europe were had - Poland(The entire Kingdom, shattered), and what is now Ukraine and Hungary(Battle of Mohi), the terrain suited their cavalry based armies.
And they were not simply fighting individual Kingdoms. There were often large alliances arrayed against them - For example, at Legnica, the Holy Roman Empire, Duchy of Bavaria, Moravia, and several Knightly Orders were on the side of Poland, yet it was a decisive Mongol victory.
Given their successes against what the layman would think of as the "more advanced" Europeans, it's easy to see where the idea of the Mongolians being unstoppable came from. Not to mention the flat out conquest of Russia.
One of the first victories against the Mongols was when Tsar Asen II of Bulgaria faced them in 1242 and was victorious, but this wasn't repeated, with the Mongols executing several successful campaigns and raids in the region up until 1279 where Tsar Ivalio forced them North of the Danube.
That was short lived due to local insurrection in 1280 leading to Ivalio's execution at the hands of the Mongols and subsequent vassalisation of his successor. This continued until the start of the 14th century when Theodore Svetoslav came into power.
As they never made it that far, we wouldn't really be able how they would fair in terrain less suited to cavalry tactics.
What I would consider the turning point in Mongol power, would not be a battle fought in Europe, but would be the Battle of Ain Jalut in 1260, in which the Mamluk Sultanate(Essentially Egypt, if you're wondering) destroyed a Mongol army of around 20,000.
This battle and its victory were born of a number of factors;
Firstly, the Mongolians had just submitted an ultimatum to the Mamluks. It was essentially, "Capitulate of be destroyed", text here;
From the King of Kings of the East and West, the Great Khan. To Qutuz the Mamluk, who fled to escape our swords. You should think of what happened to other countries and submit to us. You have heard how we have conquered a vast empire and have purified the earth of the disorders that tainted it. We have conquered vast areas, massacring all the people. You cannot escape from the terror of our armies. Where can you flee? What road will you use to escape us? Our horses are swift, our arrows sharp, our swords like thunderbolts, our hearts as hard as the mountains, our soldiers as numerous as the sand. Fortresses will not detain us, nor armies stop us. Your prayers to God will not avail against us. We are not moved by tears nor touched by lamentations. Only those who beg our protection will be safe. Hasten your reply before the fire of war is kindled. Resist and you will suffer the most terrible catastrophes. We will shatter your mosques and reveal the weakness of your God and then will kill your children and your old men together. At present you are the only enemy against whom we have to march
In the aftermath of the sacking of Baghdad, it was very clear that the Mongolians presented a distinct and existential threat to the Mamluk Sultanate. Given that the sultanate was the last Islamic "super" power in the region, this was seen by many as a fight for the existence of Islam.
As such Sultan Qutuz had the Mongolian ambassadors beheaded and declared war.
Secondly, the Great Khan Monge had just died. This gave Qutuz and the Mamluks an opportune moment in which to strike, as the Mongol Hordes in the Middle East were reduced and under secondary command while Hulegu Khan was contesting the position of Great Khan in Iran.
The Battle of Ain Julut would be decisive in the future of the Mongols in Europe and the Near East. After the the Battle, the Mamluks used their momentum and pressed Northwards to Syria, and expelling the Mamluks from the region in the First Battle of Homs. After this point, the Mongolians were effectively removed from the Levant.
Though some may find it important to note it wasn't actually the Mamluks who fought the Mongolians at Homs, it was the formerly deposed Ayyubid Princes who had become vassals of the Mamluks.
This, compounded with the Mongolian Civil War(Between the Golden Horde and Ilkhanate) eventually shattered the myth of Mongolian invincibility. In the decades following the Mongols were too tied up with internal conflicts to mount further pushes into Eastern Europe and any assaults into the region were little more than raids and were defeated if they were met on the field of battle, such as the Battle for Krakow in 1287.
Khan Nogai attempted to launch a campaign into Hungary in the 1280's, but was handily defeated by Ladislaus IV, thanks Béla IV's reforms, who had updated Hungarian military doctrine in response to the Mongol victories in 1241.
By 1294 the Mongols had splintered and lost most of their territorial gains in Eastern Europe.
If you are going to recommend Dan Carlin, then you will need to be able to critically assess what he says in his podcast, not simply telling someone to go check it out. Our rules state that you must give comprehensive, informative, and in-depth responses.
I'd like to hear from a military historian what they think would have been an effecting anti-Mongol strategy. What about heavily armoured European pike squares? European knights? Longbows? How would the creme of the European crop fare against 13th century Mongols?
Layman's question here: I heard that Mongol bows and bowstrings would quickly deteriorate in humid climates, making the conquest of some territories difficult. Is there any truth to this?
One big weakness that the Mongols faced was their inability to wage an efficient war with an island state like Japan. They tried to conquer Japan twice, once in 1274 and once in 1281. As /u/jetpacksforall stated, because the Mongols relied heavily on cavalry, they had to use their Korean tribute state as a source of ships and sailors. If the Mongols had been able to land on the mainland successfully and become entrenched they may well have succeeded, but in both cases they were repelled by a massive typhoon, which the Japanese came to call the kamikaze (divine wind). In the end, their dominance in cavalry was unmatched at sea and they paid the price in the Japan invasions.
A follow up question if I may since this discussion is about the Mongolians: how big of an impact did Subutai have in the Mongol conquests?
As a follow up question, is there any information as to the tactics that Ivaylo of Bulgaria used to drive off the mongols with an army of peasants?