Who will the next President be?

Liberal candidate Moon Jae-in from the opposition Democratic United Party is currently leading in opinion polls.

Moon was the chief of staff to former South Korean President Roh Moo-hyun and a strong proponent of the "Sunshine Policy," which attempted to improve relations between the two Koreas from 1998 to 2008.

Moon was only narrowly defeated by Park in the 2012 South Korean presidential election.

"Moon looks like the most likely candidate and unless something really unlikely happens, he'll be sailing to be the next president," Kim Hyung-a, associate professor at the Australia National University College of Asia and the Pacific, told CNN.

Would he change policy towards North Korea?

David Kang, director of the Korean Studies Institute at the University of Southern California, said that Moon was likely to seek a rapprochement with the North.

"Any of the progressives would probably be more wiling to engage with the North. Park and her predecessor were pretty hardline on the issue," he said.

The North is likely to respond better to a liberal and may actually ease its tests if dialogue, he said.

But in previous attempts at the Sunshine Policy, the North has been lackluster, according to Robert Kelly, associate professor at Pusan National University's Department of Political Science.

"While South Korea was providing assistance to the North, they kept building nuclear weapons," Kelly said.

Does Park's downfall make conflict more likely?

Tensions are particularly high at as both the North and South carry out drills on the Korean peninsula.

"North Korea is currently firing missile all over the country while South Korea and the US are conducting a series of joint exercises," said John Tierney, the executive director of the Center for Arms Control and Non-Proliferation. "And both claim they are doing so pre-emptively, so it's a very tense time there at the moment," he said.

"I don't think North Korea is going to just carry out a nuclear attack on the South, but it may, in this situation, test more conventional weapons on the edges to be more provocative."

What about the new US-made missile system?

A challenge for the new South Korean president will surround the US-made missile defense system deployed in South Korea.

Park's dismissal changes the relationship between South Korea and the United States in one big way -- the THAAD deployment just became a lot more complicated.

THAAD was due to be operational in South Korea by the end of 2017, during Park's remaining presidency, but her removal from office has thrown that into question.

But Moon, like many South Korean liberals, has questioned the value of the missile defense system to his country.

"The left doesn't think THAAD is that useful, it just provokes North Korea, but since China turned it into such a big deal now it looks like you're letting China bully you (if you stop it)," Kelly said.

The executive director of the Center for Arms Control and Non-Proliferation, John Tierney, told CNN that while Moon initially opposed THAAD, he later backed away from his comments, saying that it should be up to the next administration to decide on it.

"So he may have created enough wiggle room to change his position," Tierney said.

And what will happen to Park?

It is almost certain Park, no longer subject to presidential immunity, will face charges in the corruption scandal that led to her impeachment, says Scott Snyder, senior fellow for Korean studies at the US-based Council of Foreign Relations, told CNN.

"Clearly she is going to face criminal prosecution and it's just a matter of when," Snyder said.

It's not clear when Park will leave the Blue House, where she spent time as a child, as the daughter of former president Park Chung-hee, and as the country's first female president.