3 issues that have chilled U.S.-Russia ties

(CNN) -- The summer-long antagonism between the United States and Russia enters a new phase this week as the presidents of both countries participate in the Group of 20 nations summit.

Will discord continue? Or will some concord emerge? Although U.S. President Barack Obama and Russian President Vladimir Putin have no formal meetings scheduled, they likely will have opportunities to chat in Russia, which is hosting the gathering.

To say the two countries have been at odds this year is putting it mildly.

Edward Snowden: fugitive or refugee?

The Obama administration made former National Security Agency contractor Edward Snowden perhaps the most wanted man in the world. Snowden faces espionage charges after he admitted leaking top-secret details about U.S. surveillance programs.

The U.S.-Russia relationship became strained when Snowden was revealed to be hiding in a Moscow airport, where the Russian government allowed him to hole up in a transit zone for weeks.

Putin declined to hand Snowden over to the United States and declared Snowden a "free man" biding time in the airport.

After Snowden inquired about asylum in Latin American countries, Russia stunned Obama: it decided to grant temporary asylum to Snowden.

Angered, Obama threatened to skip this week's G20 summit in St. Petersburg. He obviously changed his mind: Obama and Putin shook hands and exchanged words briefly during the summit's opening Thursday.

It was a polite -- perhaps a tad forced -- moment, and it went no further than that.

Gay rights

Obama has often been referred to as America's first "gay president" because of his aggressive advocacy of gay rights and same-sex marriage.

Putin, however, signed a propaganda law passed by parliament that bans the public discussion of gay rights and relationships where children might hear it. Violators can be fined and, if they are foreigners, deported.

Critics say the law is so vague that someone can be prosecuted for wearing a rainbow T-shirt or holding hands in public with someone of the same sex.

Obama declared "nobody's more offended than me" by the Russian law.

Syria: Is chemical warfare for real?

The backdrop to the G20 economic summit is Obama's international campaign to begin limited bombing of Syria for the regime's alleged use of chemical weapons against its own people in a civil war.

Putin hasn't been quick to embrace U.S. assertions that Syrian President Bashar al-Assad's government is using chemical weapons. Putin wants high proof that Assad -- an ally of Russia -- has indeed engaged in such warfare.

Putin called the chemical weapon allegations "absurd" because he said the Assad regime holds the upper hand over rebels.

The skepticism is powerful because Russia is a permanent member of the United Nations Security Council and, if the United States and its allies seek U.N. approval to bomb Syria, Russia can veto such a resolution. Russia has invoked that power repeatedly the past two years.

On Wednesday, the eve of the G20 summit, Putin said he "doesn't exclude" supporting a U.N. resolution for military force against Syria -- but only if there's irrefutable proof of chemical weapons use by the Syrian government.

What's one to make of all this?

Look to history, one analyst said.

"I think Putin especially sees himself as a Cold War guy," said Julia Ioffe, senior editor of the New Republic, who was a Moscow correspondent for Foreign Policy. "He's not shed that mentality. He sees himself as a foil and counterweight to America and the world."