Miners, basically any user on the network with sufficient computing power, vie with each other to be the first to verify the new transactions and solve a cryptographic puzzle unique to that block.
Facebook is also vying for the intention of reporters, the company launched the site for journalists to serve as a place to mine for stories or other sources.
Whatever the answer, it seems like any century vying for that top spot is at a moment of great change — when the actions of our ancestors shifted humanity's trajectory for centuries to come.