What has been the role of Vice Presidents of the United States in governing and decision-making?

by Peronospora

In House of Cards (US) S02E03, Frank Underwood, newly minted as vice president, says

“There are two types of vice presidents: Door mats and matadors. Which do you think I intend to be?”

I realized I knew nothing about the role of the vice president, and how different people used the office.

Iphikrates

Not meaning to discourage anyone from trying to answer this question, but you might have better luck getting a definition of the role and responsibilities of the US vice presidency over at r/Ask_Politics.