The conflict started during the early months of 2019 and ended on July 19th, 2020 with the fall of "The Litterbox" to Coalition forces.
The war largely started due to drama in the city of Mount Augusta (MtA). The drama goes back to the existence of the FRIENDS alliance, where in particular Mir and Rhodesia would get into small disputes and fights. While the drama that happened between these groups at the time contributed to the tensions that brought on the war, the main conflict that caused it all started on January 4th, 2019. On January 4th, Baes20 (Arctikz_) who was a member of the Holy Jaded Empire (NATO) was causing trouble in Mount Augusta with two other accounts: 'LeaveMeTallone' and 'Rhiannasbutt' who were later revealed to be banned players BewsieJ and Dovah using VPN's to bypass their ban.  These three broke a few minor laws in MtA and got into a small fight with Mir. The accounts ran to bunkers owned by the HJE after being chased away.
On January 6th the Mirian 'Gregy165' went to one of HJE's bunkers near MTA and attempted to break in, but was quickly repelled by the then mysterious account 'Thomasih' - who ended up being 'poortea' on a VPN who has been banned many times for various reasons, though this was not discovered until near the end of the war over a year later. Tensions were high at this point, and rogue Mirian 'theJKH' who was just returning to the server, obby bombed a different HJE bunker in MtA around the time Gregy165 attacked Pinkerton. Mir reports to have removed both Gregy165 and theJKH at the height of the tensions to try to prevent escalation. NATO reports additional Mirians were still helping theJKH and Gregy165 in MtA. S4NTA, an officer of Mir, has said he attempted diplomacy with ComradeNick, removing Gregy165 and theJKH from Mir bunker groups but the the discussion ultimately went nowhere. On the 29th of January the NATO alliance mustered their forces with ~20 unique accounts destroying the Mir bunker in MtA throughout the night. In response, Mir considered all those that broke their bunker to be "Pearl On Sight".
On the morning of January 30th, Mir constructed a trap on the Great Overland Rail (GOR) between The Commonwealth and Mount Augusta. Later that day Mir had 'Ez2Clutch' bait NATO fighters to the trap where the rest of Mir was logged out, resulting in the pearl of Hangoverd, a NATO fighter. Mir made a post on the subreddit named "Let the Hammer Fall" essentially declaring war on NATO, being the official start date of the Mir-NATO war, on January 30th 2020. The war would continue on as the nation of Mir vs the NATO alliance, which at the time consisted of the following nations: Hallow, HJE, Polska, Tel Aviv, Annywn, Valyria and their ally Rhodesia. Later during the Ransakistan conflict a greater coalition started to form with Mir in December 2019, which would later commit fully to fighting NATO.
Siege of Pinkerton
In late January/Early February 2019, Mir launched a large scale ground attack against Pinkerton. At the time, Pinkerton was a large hole with a bunker at the center. Pinkerton was eventually taken by Mir on February 2nd.
SPQR Border Crisis
In Late February, HanTzu approached UNC leadership as a result of Mirians being suspected of setting up an attack bunker used to attack Hallow in SPQR.  The situation was initially resolved, with an official statement that the UNC would blockade both NATO and Mirian fighters. 
However, tension rose up again several weeks later when the HJE blocked the rail between Roma, the capital of the SPQR and Westminster, the capital of the Commonwealth. The rail was going under HJE territory who claimed that it represented a security threat. The grief was however removed by the UNC and the Entente.
The situation later escalated when NATO accused the SPQR of cooperating with Mir. NATO then launched an invasion of the SPQR and were relatively unopposed. Several major Roman players were pearled following the incident and SPQR cities were extensively obby bombed.
The Sieges of Sempiternal
The Sacking of Hallow
The War Broadens
In late 2019 however, the conflict intensified after LSD was attacked by the Entente and Laconia came to their aid. The Entente progressively joined Mir in their effort against NATO. NATO, on the other hand, received the help of Corvus, Laconia, and LSD.
During the first weeks of 2020, the UDF, which now included Columbia, joined the war on the side of Mir and the Entente and took part in the assault against Pinkerton after NATO took in remaining obby bombers from the War of the Coalition.
The Fall of Rhodesia
Rhodesia would fall to Mir in the first stages of the war. Rhodesian's would later group up in Columbia, starting a civil war called the Columbian Bush War, which was put down by Shadedoom and the UDF.
The Siege of Laconia
After ashnwill's vault Hotel California was attacked by SATO-Entente forces, and other fellow members of the Latvian Soccer Dogs (LSD) were attacked in various places around the map, Laconia came to LSD's aid. Laconia allowed the soccer dogs to reside within Mt. Doom, and organized an attempt to salvage the vault materials. They were intercepted on the way back home, leading to the Battle of Hotel California. Later, Laconia's capital Mt. Doom was attacked, starting the Entente-Laconia War in full swing.
Eventually NATO involvement in the defense of Mt. Doom led the Infinity War to become a world war after the Entente followed them back to the northwest quadrant after the fall of Laconia, joining Mir's war effort.
Today Laconia maintains that this element of the war is still ongoing due to no formal peace negotiations between Entente and themselves taking place.
Second Siege of Pinkerton
The Fall of Corvus
The Battle of The Crucible
The Opening of the Columbian Theater after The Battle of The Crucible
After the successful defense of The Crucible, the focus of the war shifted from skirmishes at NATO vaults to a prolonged siege of Columbian lands. NATO would quickly roll through Rotterdam, the capital of Columbia, and move onto Valyria, outside of The Crucible where they would set up fortifications. Seeing this, many more UDF, Mirian, Entente, and Coalition forces were brought to Valyria to defend the city and the vault.
In March of 2020, Valyria was obby bombed by NATO forces in an attempt to force a surrender. Two days later, Robokaiser was pearled in a skirmish in Polska, by Mirian JKH and Gregy165. After this, opposition in Polska essentially collapsed and NATO retreated back to their vaults on the world border. Eventually a skybridge would be built and Polska would be disabled as a functional military outpost for NATO, thus ending the Siege of Columbia.
Cracking the Hallow Vault
On June 27th, 2020, Coalition forces broke the Hallow Vault after a 24-hour siege. The pearl of FlashMigma was freed and ComradeRick and hockey328 were lost in the process. The pearl of Kicky was gained by Mir. The cracking of Hallow is notable as it is currently the largest vault to ever be successfully attacked and disabled.
Cracking Best Western and Vault 76
On July 18th, 2020, Coalition forces broke the Best Western vault after a another 24-hour siege. During the fight, various pearls that had been secured throughout the war were released, including those belonging to Lodish, bgbba, ComradeRick, among others. ObtainableSplat was pearled off of the skybridge but was later freed when Vault 76 was cracked. The remaining pearls that were unreleased from Best Western by Pirater were carried by Crackerjack to the Geo Vault "Litterbox".
Cracking Geo Vault & Conclusion
On July 19th, 2020, Coalition forces broke the last remaining NATO vault, the Geo vault, located by Admintown and SPQR land claims, which held the remaining SPQR pearls. With the final break of the vault, this marked the end of NATO forces and the conclusion of the war.
The Infinity War had a massive influence on server population and desire to play. Critics of the war claim that its world wide nature, lack of nuance, and effective "permapearling" of individuals resulted in a drop-off of player activity. Others claim that nobody was ever effectively permapearled during the duration of the war, and argue that most captured pearls were simply on POW status, awaiting sentencing and or release for time served until after the conflict ended.
Several nations involved in the war would die out, particularly on the NATO side of the conflict due to infrastructure destruction and pearling of citizens, but also on the Coalition side due to war exhaustion and other factors. Hallow's citizens would completely move to Realms, HJE's would do the same, and Polska would be utterly destroyed as a functioning city and state. Laconia, although several players still exist on the server, would go inactive too. Other notable nations that would cease to exist in an active capacity during the war would be Coventhia, who would drastically reduce the size of their claims and give their vault and most of their land to neutral nation Grand Imperium. New Sovia, although split by the time of the UDF/Entente's entry into the war officially, would also cease to function as a true state. Bloom, involved in the war on the side of the UDF until its departure from the alliance, would also go to Realms and go inactive.
Columbia took over stewardship of Hallow and Polska cities, and the Jaded Confederation was formed to prevent grief in HJE's cities (that no newfriends could feasibly benefit from) after an incident occured involving various individuals.
There is some evidence that server population is recovering though in the immediate aftermath of the conflict. Imperial Truidence, Icenia, and SPQR have all shown signs of a boost in activity and it remains to be seen if this will continue into the future.