Charles Reid, professor at the University of St. Thomas School of Law, recently talked to PBS News about the history and intricacies of the conclave that selects a new pope.
From the story:

The world won’t know the next bishop of Rome, apostolic successor to St. Peter the Apostle and leader of the world’s 1.4 billion Catholics until he appears before a throng of supporters in St. Peter’s Square. But in the coming days, powerful members of the Catholic Church from around the world will take part in a process that is part spiritual and part pragmatic. ...
Up until the early 20th century, Catholic monarchs asserted that they had the power to object to the cardinals’ choice for pope. “They had cardinals who would represent their interests and could veto a selection,” said Charles J. Reid Jr., a law professor at the University of St. Thomas in Minneapolis.
Pope Pius X fully prohibited the practice in 1904. “Ever since then, you’ve had this tremendous worry that someone could communicate inside the College of Cardinals and influence the outcome,” Reid said. “You want the outcome to be the pure working of the internal dynamics of the College of Cardinals.”