There are 195 sovereign states on this planet that are recognized by the United Nations and only 8 of them are not affiliated to FIFA. Here's what you need to know about them.
Vatican City
Contrary to popular belief the Vatican isn't just the pope and other high members of the Catholic Church. In fact there's enough people within the Vatican that it has it's own amateur league. Each club within the league represents a section of the city state, so we have the team of the hospital, the team of the museum workers, a team of the guards, etc.
The Vatican also has a National Team which has some interesting facts worth noting. Firstly, they sell their jerseys at the souvenir shop and a part of the proceed go to charity. Also, none of the the Vatican's home games are held in its territory due to the lack of ground, so all of the games are played in Italy in the city of Rome.
Who are the opponents of the Vatican? Usually makeshift teams such as the Austrian Journalists, Selection of UN Officials, Italian Ministry of Defense, etc. In 2014 however, Vatican City did play against Borussia Monchengladbach. It is unclear exactly what players Monchengladbach sent to the pitch but the final result was 8-1 for the Germans.
The latest news regarding the Vatican and FIFA was in 2021 when during the Euro Cup Final there was a conversation between Pope Francis and UEFA president Ceferin regarding membership but no details of the chat were ever revealed. Overall it seems like Vatican City has more important priorities than participating in World Cup Qualifiers.
Monaco
Aside from AS Monaco, the principality's only professional team that participates in the French league, and despite a population of just 36 thousand, Monaco has a national team and a league with 3 divisions. Similarly to Vatican City, the teams are mostly composed of workers of different local businesses, such as the Monte-Carlo Casino, Police Force, Monaco Hospital, etc.
3 stadiums are used for soccer in Monaco. The famous Stade Louis II is by far the most important, where AS Monaco, Monaco National Team, and other international matches are held. Than there's Stade Didier Deschamps and Stade des Moneghetti which are primarily used by the small clubs and are actually located just across the boarder into France.
Despite seemingly fulfilling every criteria, Monaco has never explicitly expressed interest in affiliating itself to UEFA and FIFA.
Kiribati and Tuvalu
These two island nations in the Pacific Ocean seem to be on their way to FIFA affiliation. To start, they are both affiliated to the OFC, the Oceania Football Confederation, which is half the battle. Even though both nations have an active league and national team, there are two main issues: infrastructure and competitiveness. Infrastructure refers to both physical structures such as a proper stadium, but also organizational structure such as youth academy's to develop talent. As for competitiveness, you can count the amount of wins Kiribati and Tuvalu have in their entire history's combined on your fingers, and they have multiple double digit losses against fellow Pacific island nations.
Either way, there definitely is interest in both Kiribati and Tuvalu to continue to grow the sport and eventually participate in FIFA tournaments.
Micronesia, Marshall Islands, Palau and Nauru
These four Pacific island nations, differently from the two mentioned above, have a long way to go for FIFA recognition. To start, none of them are affiliated with the OFC. Also, aside from the same issues that Kiribati and Tuvalu have, these four countries also have to deal with overall lack of popularity of the sport, inconsistent leagues and severe lack of funding.
Despite interest, it'll be a while, if ever, before we'll see these countries integrated into the world soccer system.