Pentagon officials say a lot of work against ISIS remains, work that Trump has signaled he would tackle with a more intense military approach -- characterized by his campaign pledge to "bomb the s--- out of them."
Analysts warn, though, that the Trump administration will have to consider a broader set of challenges, not only on the battlefields of Syria and Iraq, but beyond them as well, where a hardened military approach may not be the best way to go.
A Trump administration can't ignore the long-term challenges of ISIS affiliates spread around the world, they said. They warned that an intensified military campaign and possible increased Western troop presence could play into ISIS propaganda.
There is also the issue of the group's efforts to improve and use its chemical and biological weapons capability.
And analysts flagged the especially thorny problem of lone wolf attackers, which under a leader already known for anti-Muslim rhetoric could become an even greater risk within the US, they said.
"I fear that's going to become an even more serious problem under the Trump administration," said Matthew Henman, head of IHS Jane's Terrorism and Insurgency Center, based in London. The Obama administration has used rhetoric that stressed inclusiveness and an acceptance of Islam -- an ideological counter to ISIS efforts to make Muslims feel disenfranchised, Henman said.
Even under the current approach, though, the US has seen lone wolf attacks by people claiming affiliation with ISIS in San Bernardino, California, and Orlando, Florida.
In contrast to Obama, Trump and his national security advisor have said that fear of Muslims is rational and floated the idea of banning Muslim immigration to the US. That rhetoric plays into ISIS recruitment efforts, Henman said.
In terms of the "demographic in the US that is at risk of being more disenfranchised, made to feel less welcome, made to feel more segregated and hated in America, you're potentially going to have a bigger pool of people willing or more susceptible to the message of radicalization and recruitment that the Islamist State is advancing," Henman contended.
For now, within Syria and Iraq, the US is painting a picture of progress against ISIS, also known as ISIL.
Lt. Gen. Stephen Townsend, commander of the Joint Task Force-Operation Inherent Resolve, told reporters Wednesday that the story of anti-ISIS efforts has changed radically since 2014, when the Iraqi army was on the run and the US was focused on "helping our partners halt ISIL's relentless onslaught."
In 2016, Townsend said, "our campaign is all about the counter-offensive, liberating terrain and the population in Iraq and Syria from the clutches of ISIL's brutal control."
But even after coalition-backed Syrian and Iraqi troops liberate Mosul, Iraq and ISIS's self-proclaimed capital of Raqqa, Syria, Townsend said, "there is still a lot of work to be done."
Among the ongoing concerns the Trump administration will have to deal with is ISIS' chemical-biological weapons program.
"They have demonstrated a capability, they've demonstrated a willingness to use it," Townsend said.
The Obama administration has recently added to the trainers advising and assisting the Syrian and Iraqi fighters, but Trump and his aides have made clear that they want to bolster the military response even further.
Trump's incoming national security adviser, retired Lt. Gen. Michael Flynn, has told Fox News that one of the problems with the current fight against ISIS is that the military's "hands are tied."
Henman noted that "there's plenty of fighting still to do." ISIS' recent recapture of the Syrian city of Palmyra suggests that substantial numbers of fighters remain, Henman said.
The fight won't just be in Iraq and Syria, either. Trump will also have to address the ISIS affiliates that have spread to North Africa, Afghanistan and elsewhere in the Middle East.
"The problem is now we have these groups that are not just groups claiming affiliation, they ARE the Islamic State," Henman said, using another term for ISIS. "Even if you wiped out every single last IS fighter in Iraq and Syria, the organization continues. They can boast that the Caliphate project continues."
Intensifying the military campaign as Trump has talked about, he said, could lead to more civilian casualties. And that could give ISIS another recruitment tool even as they are now having trouble replenishing their numbers, according to US anti-ISIS coalition envoy Brett McGurk.
Then there's the question of budgets.
Julianne Smith, senior fellow and director of the strategy and statecraft program at Center for a New American Security, said the Trump team would "have to determine how far they're willing to take this -- what kind of resources do they want to dedicate to the problem."
"We're obviously spending a lot of money on the current operation," she noted. "If they want to intensify the effort, they first have to ask themselves, are we willing to make the case to the American public that we want to double down?"
She added, "My suspicion is that they'll end up very close to current policy, given what he said during the campaign, where the American public is on this and where our coalition partners are."
And some problems can't be solved by an airstrike campaign, or even the application of force.
Daniel Serwer, who directs the conflict management program at the Johns Hopkins School of Advanced International Studies, said that that as the US-backed Syrian and Iraq forces rack up victories against ISIS, the group will likely return to insurgent tactics which require a different response.
"We are already bombing the s--- out of them," Serwer said. "After the fall of Mosul and Raqqa, they will return to insurgency and we won't be able to find and target them so readily."
The issue the Trump administration will have to focus on then, he said, is how well the liberated areas are governed.
While "the Iraqis haven't done too badly on that score" in Sunni-dominated towns without significant ethnic or sectarian cleavages, areas like Mosul with mixed populations "are going to be much more difficult. Governance failures would allow ISIS or worse to return," Serwer said.
The Trump administration will also face a tricky situation in Raqqa that can't be resolved with military force, Henman and Serwer pointed out.
Kurdish allies of the US, the YPG, and the Syrian Democratic Forces are "pretty much in direct competition with the Turkish army and Turkish-backed proxies in northern Syria," Henman said.
"There we have nothing like the agreement among the different forces attacking Mosul," Serwer pointed out. "Without an agreement, tragedy could ensue."