Since forming their own nation, the X-Men have left the world of heroes and villains behind for a new life in a world where the island Krakoa is geo-political powerhouse with relationships with nations all around the Marvel Universe. This conflict arose out of the many changes to the world that came with the creation of Krakoa and its miracle drugs.
While the X-Men have formalized relations with most of the world and some nations, like Wakanda, have avoided any contact or relations with the mutant nation, other countries have taken several steps to deter the X-Men's current rise to power and to use Krakoan advances to their own ends and purposes. And considering how many nations have already attacked Krakoa, the X-Men seem well on their way into turning their collective skirmishes into a global conflict.
LATVERIA
Given his tendency to manipulate any situation for his own advancement, it would make sense for Doctor Doom to see Krakoa as both a threat and an opportunity. In the pages of X-Men/Fantastic Four, by Chip Zdarsky and Terry Dodson, Doom has made his presence known in the ongoing conflict between the X-Men and the Fantastic Four over the future of Franklin Richards and his mutant powers.
Besides lecturing Xavier on his approach to world politics, Doom seems interested in starting a war with the mutant nation of some kind, having placed all Latverian mutants on his own island and tricking Wolverine into killing a Latverian soldier. Doom's true intent in saving Franklin's dwindling power is still unclear, as he unleashes an army of Doom sentinels to clear his land of all intruders.
TERRA VERDE
A small nation, Terre Verde began on harsh terms with Krakoa, as the country had hoped to build its name in the field of telefloronics, something that became obsolete overnight when compared to Krakoan technology. Although the X-Men were able to reach a treaty with the nation, several members of the country had become exposed to their own research, becoming human-plant hybrids.
At first thought to be a victim of these creatures, Hadwin Cocom, the son of the nation's president, was actually revealed to be the instigator of these events. Seeing the potential for a new kind of Omega Sentinel, Beast used X-Force to kill the infected and remove Hadwin's memories. Unfortunately, Hadwin's determination to remove Krakoa remained and his creatures took control of the nation in Benjamin Percy and Joshua Cassara's X-Force #9.
RUSSIA
When Krakoa first introduced themselves to the world, a series of embassies, with their own portals to the X-Men's home, were placed in strategic locations. One of these portals was found in Russia, who did not respond kindly to the X-Men taking a piece of their land and offering to take their citizens. Making the choice to cut off any access to the Krakoan portal, Russia's contact with the mutants has been reserved to the affairs of the Marauders and X-Force.
While some mutants, like Colossus, have focused on rescuing mutant refugees from Russia, other mutants have noticed Russia's increased use of anti-mutant technology in their weapons, which was originally developed by Forge. Some soldiers have been equipped with mutant-dampening suits as a means to battle the X-Men. This technology has also tied Russia to the Homines Verendi.
MADRIPOOR
Madripoor has long been a nation for the lawless with its goals being directed by its current leader. Its past leaders have included Viper and Mystique, who have both had ran into trouble with Wolverine and the X-Men. Now, the island has become the territory of the young Hellfire Club, which is comprised of aristocratic and sociopathic children. However, since that name has been retaken by Krakoa, this group refers to themselves as the Homines Verendi.
Given their wealthy status, this group has been working to be the premier anti-mutant resource on the black market. Whether through their technology or information, the Homines Verendi are determined to profit off the downfall of the mutant nation. With their resources and a fearless leader in Kade Kilgore, this nation promises to be a large threat in the X-Men's future.
CARNELIA
For some nations in the world, the notion of mutants still fills humanity with fear and thoughts of aggression. In the case of Carnelia, this nation has no interest in building any relationship to Krakoa. Although this nation has made no direct moves against mutantkind, one of their citizens has already immersed the X-Men in another potentially fraught political situation In Jonathan Hickman and Flaviano's New Mutants #9.
This citizen is a young girl named Natashia "Tashi" Repina whose reality-warping power rivals that of the Scarlet Witch. With her ability to warp reality and a complete lack of control over those powers, her potential for destruction could lead Carnelia to place the blame on Krakoa. Even though a group of experienced New Mutants is on the scene, they've already had to call in back up from some unlikely allies.
SOKOVIA
Since debuting in the Marvel Cinematic Universe, the nation of Sokovia has also experienced a tumultuous history in the main Marvel Universe too. After years of war and inner-conflict, the nation fell under the control of the Red Skull and Hydra in the lead-up to Secret Empire. After Hydra was defeated, Sokovia has taken steps to repair their status in the world.
Welcoming Professor X in celebration of their treaty, the leader of Sokovia poisoned Xavier with their toast in Benjamin Percy and Joshua Cassara's X-Force #1. Shortly after this, Xavier was shot and killed on his return home, and it looks like Xavier was slipped a tracking device by the Sokovians, which helped XENO's Reavers track him down. Sokovia's ultimate reasoning for this betrayal has not yet been revealed, but it is a reminder that not every foe to Krakoa will attack with weapons as big as Sentinels.