Stolen:
The fact remains that swords continue to be used by some military units even today.
In particular, the Force Reconnaissance Battalion of the Philippines’ Marine Corps and the Special Action Force continue to arm their soldiers with blades, like the ginunting and the bolo.
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Ginunting
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Bolo
I consider the ginunting and the bolo to be swords, albeit short ones; I understand, however, that some might consider them to merely be very long knives. For this answer, knives are considered to be blades that around 9″ (~23cm) or shorter. The ginunting and the bolo, on the other hand, can reach up to 20″ (~51cm) and ~13″ (~33cm) respectively, making them around twice as long as what might locally be considered knives.
These swords continue to be used regularly in the low-intensity conflicts that take place in the jungles of the Southern Philippines for a number of reasons. For one, the thick jungles of Mindanao in which they operate facilitate - in fact, they demand - ambushes at close quarters. The dense foliage inhibits the use of firearms by limiting lines of sight, breaking up fields of fire, and providing an overabundance of cover and concealment to all parties. This is further coupled by the fact that the foliage severely limits visibility. Furthermore, the dense jungle greatly enables swift and effective withdrawals: the separatists and terrorists can very easily disappear into the green at the first sign of trouble.
The terrain thus demands the use of blades. The Marines’ adversaries are likely to utilise the blade in ambush attacks for a variety of reasons. For one, blades are relatively easier to procure than a gun. Furthermore, they can be extremely effective, both kinetically and psychologically, especially when its wielder has already been drugged up under a chemical cocktail, as terror groups are wont to do these days. Most crucially, blades are silent, and do not draw attention like firearm reports.
Because their adversaries are very likely to have already closed the distance and have already deployed their blades in the event of an ambush, the Marines are also forced to deploy their blades instead of their firearms, which are less effective at extreme close quarters. The Marines are also incentivised to utilise blades through the same logic: they can strike swiftly and silently in ambushes without alarming their quarry.
The question that must become obvious at this point is this: if blades are highly useful under such circumstances, why swords instead of knives? Also, why are swords less prominent in other forms of conflicts and battlefields?
Swords of this variety remain the more useful tool as compared to knives under such circumstances because they occupy a particular niche. They are significantly longer than - around twice the length of - most knives, and yet are not that long so as to become unwieldy in thick jungles. The range advantage gained by an individual with a weapon that is around twice as long as that of his adversary’s is considerable. Furthermore, unlike knives, their blade shapes do not just enable the thrust, but also facilitates the slash. The forward curving blade of the ginunting, and the heavy tip of the bolo, are both evidence of this. While there exists knives that also do facilitate the slash, such as the kukri, they nevertheless lack the range advantage that a sword offers. It is for these reasons that swords are preferred to knives under such circumstances.
Swords feature less prominently in the tactics, doctrine, and operations of other militaries and military units for a number of reasons. Swords, and the use of swords, are deeply rooted in a specific geocultural context. Most militaries and societies no longer use blades to the same extent as the Filipino military and society does. While plenty of militaries and military units continue to emphasise the use of the blade, their use of the blades remain limited to what are generally considered knives. (Unless you’re from the The Rifles, in which case you call your bayonet a sword.) This might be because their indigenous sword-culture are less suited for the kind of operations and terrain that their militaries engage in.
Furthermore, both terrain and mission profiles have to agree in order for the use of blades to be viable. The terrain has to both enable and encourage the use of blades, and the mission profile has to at the same time be at least permissive of the use of lethal force. There are stories of Filipino operators who head into the jungles to hunt the heads of their enemies, literally beheading them with a slash of their blade. Most modern conflicts and battlefields enable and encourage, in one way or another, the use of firearms and other munitions. The dense Southeast Asian foliage, however, does not.
To sum up, swords continue to be used in some military conflicts today. Whether they are used, however, greatly depends on factors like culture, and a confluence of terrain and mission profiles.