Divisions also remain within NATO over the question of alliance enlargement and its relationship with Russia - two issues which have become inextricably entwined.
NATO leaders at a summit in April 2008 agreed that Georgia and Ukraine would join the alliance at an unnamed point in the future.
The agreement was meant to keep the peace between members who wanted to see the former-Soviet republics join as soon as possible, such as the US, Britain and Poland, and those who warned that such a move would enrage Russia, such as Germany and Italy.
But Russia's invasion of Georgia a year ago, and its gas rows with Ukraine, have made Eastern relations a hot topic once again, with some members calling for closer ties with Moscow, and others accusing the Kremlin of trying to build a sphere of influence in Europe.
Fogh Rasmussen therefore faces the unenviable task of trying to forge alliance agreement on how to deal with the former-Soviet trio.
He will also have to find a new balance of power between NATO's heavyweights, the US, Britain, France and Germany, after France rejoined the alliance's military command after a 40-year absence.
And he will have to do all that while he tries to impose his own vision on NATO's future, with insiders saying that he will push to make the organisation more efficient, transparent and media-savvy.
That is to say nothing of the unexpected international crises which are likely to come his way.
Whatever else awaits Fogh Rasmussen in the next four years, the future certainly looks busy for the twelfth NATO secretary general.