Mexico began the century under the rule of the now elderly Porfirio Diaz. But Diaz was not able to keep up with changing times, and the fall of his rule is the opening chapter of the Mexican Revolution.
The early years of the century saw two important comets and the biggest meteorite strike on the Earth in recorded history. There was also a lot of attention paid to the planet Mars, amid speculation that Mars might be home to life. Maybe even intelligent life.
Roosevelt had pledged not to seek another term as President, and was concerned that his successor preserve and build upon his Progressive legacy. He chose William Howard Taft as his political heir, but after Taft's election, the two men would part ways.