As the governing body of association football, FIFA is responsible for maintaining and implementing the rules that determine whether an association football player is eligible to represent a particular country in officially recognised international competitions and friendly matches. In the 20th century, FIFA allowed a player to represent any national team, as long as the player held citizenship of that country. In 2004, in reaction to the growing trend towards naturalisation of foreign players in some countries, FIFA implemented a significant new ruling that requires a player to demonstrate a "clear connection" to any country they wish to represent. FIFA has used its authority to overturn results of competitive international matches that feature ineligible players. 

FIFA's eligibility rules also demand that in men's competitions, only men are eligible to play, and that in women's competitions, only women are eligible to play. 

Historically, it was possible for players to play for different national teams. For example, Alfredo di Stefano played for Argentina (1947) and Spain (1957–61). 

Di Stefano's Real Madrid teammate Ferenc Puskás also played for Spain after amassing 85 caps for Hungary earlier in his career. A third high-profile instance of a player switching international football nationalities is Jose Altafini, who played for Brazil in the 1958 FIFA World Cup and for Italy in the subsequent 1962 FIFA World Cup.
What is FIFA
of what?
What do Americans call this sport?
What is one thing they do?
for what?
How did they decide if a person could play for a national team before?
When did this change?
Why?
How do they decide now?
What do they do if a match has someone that should not be playing?
Has anyone ever played for more than one national team?
Who was one such person?
Who did he play for?
What else does FIFA say about men's competitions?
What professional team does Puskas play for?
And he has played for what countries?
Did Altafine play in more than one World Cup?
when?
What countries?
How often is the World CUp?
governing body
governing body
association football
association football
soccer
 20th century
maintaining and implementing the rules
 maintaining and implementing the rules
eligibility
eligible
citizenship
citizenship
In 2004
In 2004
in reaction to the growing trend
 in reaction to the growing trend
clear connection
clear connection
overturn results
overturn results
yes
different national teams
Alfredo di Stefano
Alfredo di Stefano
Argentina and Spain
Argentina
only men are eligible
only men are eligible
Real Madrid
Real Madrid
Spain and Hungary
Spain
yes
 instance of a player switching
1958 and 1962
1958
Brazil and Italy
 Brazil 
unknown
unknown