Trump running-mate, Indiana Governor Mike Pence, stated that his model for the vice presidency is the Cheney model. There are many possible ways to interpret this statement.
The initial take is that it is ham-handed, since there are not tons of Cheney fans around (although the Cheney haters weren't going to be voting Trump anyway). But maybe, it is a secret message that really Pence would be running things.
That is also unlikely. Probably Pence is simply saying he would be an active and engaged vice president, like Cheney. Of course for a Vice President Pence to exercise any influence, Trump would have to listen to him. It is not clear if Trump listens to anyone.
For all of its political freight, the Cheney model is overstated. Cheney was a difference in degree not kind from his predecessor. He had a larger national security staff than Gore, but at the expense of his domestic policy and political staff. Cheney sat in on lots of meetings that VPs had not previously sat in on. But no specific case where he pushed a policy the president did not care for has emerged.
Perhaps that is the most significant point. Cheney did the president's bidding. He aired his thoughts, but there are innumerable instances of President Bush rejecting Cheney's preferred position.
Finally, Cheney was also, by all accounts, incredibly deferential to the president.
Decades earlier Cheney had been chief of staff to President Ford. In an odd way, Cheney was a sort of super-chief of staff to President Bush. Involved in everything, enforcing the president's will, sharing political and policy intelligence.
In that sense, because Trump will bring a depth of inexperience unknown in the modern presidency, the Cheney model might be dead on for a VP Pence. He will need to get involved in everything, as the President will bobble the ball on issue after issue.