Here’s a look at the top four candidates for National Security Adviser in the wake of Michael Flynn’s resignation and retired Vice Admiral Robert Harward’s decision not to accept the post. According to administration sources, Keith Kellogg, David Petraeus, Keith Alexander, and Jim Jones are all under consideration.

Keith Kellogg: Retired Lt. General Keith Kellogg is currently serving as the Acting National Security Adviser so, naturally, he is seen as a top candidate for the post.

Kellogg is also the current chief of staff for the National Security Council, making him second to Flynn before the latter’s resignation.

72-year-old Kellogg is a Vietnam veteran with an extensive resume of military service, summarized by the White House as follows:

General Kellogg is a decorated veteran of the United States Army, having served from 1967 to 2003, including two tours during the Vietnam War, where he earned the Silver Star, the Bronze Star with “V” device, and the Air Medal with “V” device.  He served as the Commander of the 82nd Airborne Division from 1997 to 1998.  Prior to his retirement, General Kellogg was Director of the Command, Control, Communications, and Computers Directorate under the Joint Chiefs of Staff.

Fox News recalls Kellogg surveying the beautiful weather and stirring march of paratroopers that greeted him when he took command of the 82nd Airborne and remarking, “I think today just proves with this great day that God must be a Tar Heel and a paratrooper.”

His wife Paige Cook is also a veteran paratrooper who served in Grenada. Heavy.com quotes General Kellogg on how his wife reacted when they learned the 82nd Airborne would be deployed in Saudi Arabia after Iraq invaded Kuwait: “She said, ‘This is serious stuff. You get on an airplane. You don’t worry about me.’”

Kellogg was the chief operating officer for the Coalition Provisional Authority in Iraq — in other words, the post-Saddam Hussein provisional government — in 2003 and 2004. He was also chief of staff for the head of the Coalition Provisional Authority, Paul Bremer. His work in Iraq solidified his reputation as an “expediter” who knows how to cut through red tape, as his colleagues told the L.A. Times.

An example of the perspective Kellogg gained from working in Iraq is the op-ed he wrote for Fox News with Mike Flynn last October, concerning the operation to liberate Mosul from the Islamic State. Kellogg and Flynn criticized the Obama administration for telegraphing the U.S. coalition’s moves in Mosul, giving ISIS too much time to prepare its defenses.

They also feared that Iran was gaining far too much influence through its operations in Iraq and Yemen:

Under the Obama/Clinton administration, Iran has become the dominating and aggressive player in the Middle East. Iran’s influence stretches from Afghanistan to Syria, to Iraq, Lebanon, and Yemen. Hillary Clinton’s failed foreign policy, her initiation of the disastrous Iranian nuclear deal, and overall bad judgment as Secretary of State allowed and emboldened Iran’s influence in the region.

Kellogg’s critics evidently plan to treat his experience with the provisional government of Iraq as a negative against him, should he receive the National Security Adviser appointment. He’ll also be attacked for his involvement with military contractors such as Oracle, Cubic Defense, Analex, Raytheon, and Abraxas. CNN lays out this strategy in so many words: “As more scrutiny draws on Kellogg, he is sure to face pushback for his roles in the private sector and the Iraq War.”

His supporters will point to that same resume as evidence he’s an information-warfare visionary with a unique understanding of both traditional military operations and unconventional warfare.

Despite his impressive resume and current position as Acting National Security Adviser, many observers describe him as a long shot for the permanent spot; retired General Barry McCaffrey, a longtime acquaintance, flatly told Politico, “he won’t be the selection.”

David Petraeus: Appointing Petraeus would seem like an unusual move for an administration seeking to recover from controversy as he lost his position as CIA director in 2012 after improperly sharing sensitive material with his biographer and mistress, Paula Broadwell.

President Trump reportedly thinks well of Petraeus, having considered him for secretary of state and even vice president, according to CNN. The tragedy of his downfall after the Broadwell affair is that he was a military leader of remarkable accomplishments, most famously the “surge” in Iraq.

Petraeus was endorsed as “very qualified” and a “terrific” candidate for National Security Adviser on Wednesday by none other than Paula Broadwell. In a CNN interview, she noted it has been five years since the scandal over Petraeus sharing sensitive information with her, and it was time for everyone to move on. She, however, she felt there was a double standard in play and that she has been treated more harshly than Petraeus.

“I think a lot of what happened to him has been taken out of context. There was no ill intent and again, no national security was jeopardized in any way. He’s paid a price for it,” Broadwell said.

Writing at National Review, David French applauds Petraeus’s accomplishments and labels him an “American hero, one of the great generals of modern times” for what he accomplished in Iraq, but nevertheless argues it’s time for him to “exit the public stage” because of the actions that removed him as CIA Director. 

Among other things, French says it would be “breathtaking cynicism” for Trump to tap Petraeus for National Security Adviser after criticizing Hillary Clinton for similar offenses so sharply during the 2016 presidential campaign.

U.S. News and World Report notes that Petraeus remains under criminal probation until April after pleading guilty to a misdemeanor charge of mishandling classified information.

Keith Alexander: Alexander is a West Point graduate and retired four-star Army general who most recently served as director of the National Security Agency. He also headed up the U.S. Cyber Command, where he was “responsible for planning, coordinating, and conducting operations and defense of Department of Defense computer networks,” as described by his NSA bio.

Alexander holds degrees in business administration, systems technology / electronic warfare, physics, and national security strategy. His experience with cyber-warfare will undoubtedly loom large in President Trump’s assessment.

Alexander’s assessment of President Trump on cybersecurity is strongly positive. Fortune describes his praise of Trump:

Speaking at a breakfast in San Francisco on Tuesday morning, retired General Keith Alexander described a recent meeting at which the President discussed cybersecurity issues with members of his inner circle. According to Alexander, Trump’s behavior shifted significantly once members of the media left the event.

“The President’s demeanor changed to what you would expect of a corporate CEO,” said Alexander. “The part that struck me was he listened. He took what they said, restated it, went on to next thing and allowed everyone to talk.”

The gathering reportedly included Trump, adviser Jared Kushner, Defense Secretary James Mattis, former New York City mayor Rudy Giuliani, and others.

Alexander also said Trump’s comportment in the meeting was “the president our nation needs to see,” and expressed confidence Trump would be able to develop a comprehensive strategy to combat cyber threats.

That was the morning of the day Mike Flynn resigned, so Alexander certainly understood the narrative of White House chaos he was pushing back against. He made similar points in an interview with Bloomberg Politics, saying that Trump was keeping his campaign promise to take cybersecurity seriously.

At the meeting in San Francisco, he laid out some interesting perspectives on information warfare, including his belief that “hacking back” against state-sponsored hackers was a mistake. He fears the United States would be so effective at retaliatory hacking that targets like North Korea would escalate swiftly to real-world warfare, so efforts are better directed to developing strong computer defenses. He also thinks the government should work closely with private industry to resolve issues such as the commercial availability of unbreakable encryption.

After retiring as director of the NSA in March 2014, Alexander founded IronNet Cybersecurity, where he is currently the Chief Executive Officer. A profile at Foreign Policy described IronNet’s technology as a “system to detect so-called advanced persistent threats, or hackers who clandestinely burrow into a computer network in order to steal secrets or damage the network itself.”

“Alexander is believed to be the first ex-director of the NSA to file patents on technology that’s directly related to the job he had in government,” Foreign Policy added, noting that both private and government lawyers worked to ensure all of IronNet’s patents were legal and did not infringe on NSA intellectual property. Bringing him back into the government as National Security Adviser would give the Trump administration an opportunity to put the expertise he has developed in the private sector at the service of the American public.

Jim Jones: Jones is the former Supreme Allied Commander in Europe, leading all military operations for the North Atlantic Treaty Organization — clearly a great resume enhancement for the Trump administration, given the president’s past criticism of NATO. He is the first Marine to hold the position of Supreme Allied Commander.

He was also Marine Corps commandant, a graduate of both the Amphibious Warfare School and the National War College. He commanded operations in Iraq, Turkey, Bosnia-Herzegovina, and Macedonia, and is a decorated veteran of the Vietnam War. 

He commanded a Marine expeditionary unit during Operation Provide Comfort, which brought relief to Kurds in Iraq after the Gulf War. This would provide both valuable insight and good connections as the Kurds continue to figure prominently in U.S. policy for Syria, Iraq, and Turkey. He recently published an article written from that very perspective at Foreign Policy.

Perhaps most pertinently, Jones has already served as National Security Adviser under President Barack Obama, from 2009 to 2010. Obama replaced Jones “after concluding that the general was a bad fit for the administration,” as the New York Times very delicately puts it. Other accounts are far less delicate.

In his book The Amateur, author Ed Klein describes Jones’s tenure as “19 torturous months” and says he “became a victim of a bunch of snarky Obama-ites in the White House who resented the fact that he wasn’t a member of the inner circle.” According to Klein, Jones was particularly upset that he was never allowed to see the president without being surrounded by Obama political people and clashed with some of them when he felt they were disparaging the military.

CNS News notes Klein’s account is supported by Bob Woodward’s book Obama’s Wars, which quotes Jones comparing the excessive number of aides surrounding Obama to “water bugs.”

This could mean that Jones will be eager for another shot at the National Security Adviser position, in a more supportive White House environment — or that he’ll be reluctant to enter a White House frequently denounced as chaotic and tumultuous by the media and potentially repeat his bad experience from 2009.

Jones is currently the head of a consulting firm, Jones Group International, which specializes in foreign policy, national security, and energy security.