All eyes in the political world will be fixed on Hofstra University in New York Tuesday night, where President Obama and Mitt Romney will debate for a second time.

Second presidential debates present unique opportunities. For the candidate coming out of the first debate with momentum (in this case, Romney), it’s a chance for an encore on a national stage. For the candidate who struggled the first time around (Obama), it’s a do-over.

The format of debate No. 2 is the town hall, where voters will pose questions to the candidates directly. That means Tuesday will be about more than politics and policy. The way the candidates interact with the voters and who appears to connect more is equally important.

Here’s a look back at the last five second presidential debates, and how each impacted (or didn’t) the race that year: 

* 2008: McCain needs a big win, doesn’t get one

Headed into debate No. 2, Sen. John McCain (R-Ariz.) needed a good showing. There was no clear winner in debate No. 1, and as the financial crisis had seized the nation’s attention, Obama was building momentum in the campaign.

The town hall debate at Belmont University in Nashville seemed an ideal setting for McCain to make gains. After all, he had challenged Obama to a series of town hall debates earlier that year.

McCain received attention in Nashville, but not the type he was looking for. He referred to Obama as “that one” at a point, sparking a lot of post-debate speculation about why he did that – speculation that drowned out whatever policy distinctions McCain was hoping to draw. Post-debate polling of debate watchers indicated an Obama win.

* 2004: Bush does better in Round 2

Comparing Obama to George W. Bush may seem odd, but the current president’s predicament coming out of the Oct. 3 debate bears some similarities to 2004. Sen. John Kerry (D-Mass.) was viewed as the winner of the first debate and the Democrat had built some momentum coming out of it.

The debate was filled with national security and foreign policy questions, including a heated response from Bush after Kerry suggested he wasn’t “going to go alone like this president did.”

“Tell Tony Blair we're going alone. Tell Silvio Berlusconi we're going alone,” responded Bush.

Bush did better in the second debate than the first one, even if there was no clear winner at the St. Louis showdown. The Republican won reelection in November, a reminder that a rough start to debate season doesn’t necessarily spell the end of the world for an incumbent.

* 2000: The least memorable of the three debates?

In debate No. 2 – arguably the least memorable of the three that year – Vice President Al Gore dialed back the sighing and body language choices that came across as condescending to some in his first debate against George W. Bush, a reminder that second debates are often about course corrections.

The first debate was notable for Gore’s sighs, and who can forget the moment in third debate (see below) – a town hall – where Gore strolled up to Bush, appearing to try to intimidate him.

* 1996: The “age” question, at the second of two debates

There were only two debates in 1996, and in the second and final one, former Republican senator Bob Dole of Kansas sought to play offense against incumbent Democrat Bill Clinton over ethics. But Clinton stuck to the script and cruised to reelection in November.

In one of the debate’s more memorable exchanges, Dole’s age – he was 73 at the time – came up, and the Republican drew some laughs when he said: “Wisdom comes from age, experience and intelligence. And if you have some of each; and I have some age, some experience and some intelligence, that adds up to wisdom.” Clinton said he didn’t think Dole was too old to be president but added, “It’s the age of his ideas that I question.”

* 1992: George H.W. Bush checks his watch

This debate is a perfect example of why the town hall format matters. George H.W. Bush checked his watch as a member of the audience started a question about the personal impact of the nation’s debt. This is exactly not the kind of attitude (voters must have wondered: Did he have somewhere better to be?) candidates want to project at town hall debates. We also included the clip in our 10 most memorable debate moments overall, illustrating how powerful it was.