WASHINGTON — Brittney Griner. Austin Tice. The Citgo 6. And now, potentially, three American military veterans who were captured by enemy forces after traveling to Ukraine to fight Russia.

They are among nearly 50 Americans who the State Department believes are wrongfully detained by foreign governments. At least a dozen more Americans are being held as hostages — including by extremist groups — or on criminal charges that their families dispute.

American citizens are increasingly attractive targets for U.S. adversaries — including China, Russia, Iran and Venezuela — looking to use them as political pawns in battles with the United States.

Ms. Griner, a professional basketball player, is perhaps the most high-profile American to be snared by what the State Department has called dubious charges. She was detained in February at an airport near Moscow after authorities said they found hashish oil in her luggage. Her arrest came just days before Russian forces invaded Ukraine, which is being armed by the United States and its allies.

This past week, Jake Sullivan, the White House national security adviser, said the Biden administration would continue to work to make sure that Ms. Griner, Paul Whelan — another American held by Moscow — and “all unjustly detained Americans and hostages are home safely.”

Here is a look at “wrongful detentions,” as they are known, and some of the struggles of Americans held overseas.

What does ‘wrongfully detained’ mean?

Generally, an American who is held by a foreign government for the purposes of influencing U.S. policy or extracting political or economic concessions from Washington is considered “wrongfully detained.” In these cases, negotiations between the United States and the other government are key to securing the American’s freedom.

The State Department does not release the precise number of Americans that it has determined are in that category. But a senior State Department official said there were 40 to 50 wrongfully detained Americans abroad.

“Hostage” is a blanket term used to describe Americans who have been blocked from leaving a foreign country. Some are held by terrorist organizations or other groups with whom the State Department does not have diplomatic relations. In these cases, the F.B.I. and other intelligence or law enforcement agencies lead negotiations.

According to the James W. Foley Legacy Foundation, named for a journalist who was killed in Syria by the Islamic State in 2014, 64 Americans are wrongfully detained abroad or being held hostage.

How long have some of the Americans been held?

A wrongful detention can span a few days or weeks, or last years. One of the longest-detained Americans is Mr. Tice, a freelance journalist who was captured in Syria in 2012. U.S. officials believe he is being held by the Syrian government, which denies it.

In a CBS News interview on Wednesday, Mr. Tice’s parents urged the Biden administration to meet with Syrian government officials even though diplomatic relations between the two countries have been formally suspended since 2012. “That’s what’s going to bring Austin home,” said his mother, Debra Tice. President Biden met with Mr. Tice’s parents in May and promised “to work through all available avenues” for his release, according to a White House statement.

Siamak Namazi, an American detained in Iran, said last month that the Iranian government would apparently free him and its other captives, including his father, only if the Biden administration offered “sufficient incentives.”

“Tehran seems to be demanding more for our release than the White House can stomach,” Mr. Namazi, who has been held in Iran since 2015, wrote in a guest essay for The New York Times.

What is the State Department doing to get them released?

The State Department’s Office of the Special Presidential Envoy for Hostage Affairs handles negotiations for wrongfully detained Americans.

The office has grown to about 25 negotiators and other officials in recent years, up from five, as more Americans are detained by foreign governments. Each case is assigned an expert on the country where the person is being held.

The process is extremely difficult, said the senior State Department official, who spoke on the condition that he not be named to describe some functions of the office.

All of the foreign governments that are detaining Americans have, at best, rocky relations with the United States. In some cases, like Iran, messages are sent through other governments that serve as intermediaries; in others, U.S. officials work through levels of the foreign government’s bureaucracy to get to someone senior enough to influence a decision.

The communications are intended to reinforce the consequences of continuing to hold Americans captive, the official said.

He said foreign governments often felt as if they were the aggrieved party and usually began with demands that he called unreasonable.

The State Department does not provide legal assistance to the detained Americans or their families.

Does the United States pay ransom or swap prisoners?

A 2015 directive by President Barack Obama prohibits promising “ransom, prisoner releases, policy changes or other acts of concession” to bring detained Americans home. The policy takes away key incentives for hostage takers to detain Americans in the first place and prevents the exchange of U.S. revenue or other resources that could be used for other nefarious activities, the document notes.

But there have been numerous prisoner swaps with foreign governments to free detained Americans — most recently Trevor Reed, who was held for more than two years in Russia before his release in April. A Russian pilot who was imprisoned in the United States on cocaine trafficking charges was simultaneously released as part of the negotiations.

Mr. Reed had suffered from tuberculosis while in prison, making his case all the more urgent.

Similarly, U.S. officials late last month tried to persuade the Venezuelan government to release Matthew Heath from an underground prison cell for humanitarian reasons after his family said he had tried to kill himself. President Nicolás Maduro of Venezuela has refused, although he freed two other Americans in March.

Iran is holding Mr. Namazi and three other Americans while Tehran negotiates with world powers over limiting its nuclear program. The chief U.S. negotiator, Robert Malley, has said the fate of the detained Americans is not directly tied to the talks.

“But I will say it is very hard for us to imagine getting back into the nuclear deal while four innocent Americans are being held hostage by Iran,” he told Reuters in January.

Does public pressure or other publicity help?

It depends.

In some cases, major displays of public pressure might not help matters, the senior State Department official said. Fear of provoking an already hostile government is among the reasons negotiations are conducted in secret.

Family members of many wrongfully detained Americans also are cautious about discussing the details of cases as relayed to them by the State Department or other officials — partially for security reasons and partially to ensure the U.S. government does not hold back any updates.

But some have set up advocacy networks to pressure the U.S. government to negotiate more aggressively and, above all, to make certain that their loved ones are not forgotten.

“We wake up every day knowing that they are suffering far more than we could imagine — so much so that many of them dread waking up at all,” the relatives of 19 Americans captured abroad wrote in a letter to Mr. Biden in June.

Ms. Griner used the public attention to her case to ask Mr. Biden to intervene not just on her behalf, but also on behalf of other Americans who are wrongfully detained.

“I realize you are dealing with so much, but please don’t forget about me and the other American detainees,” she said in a handwritten note to the president this month. “Please do all you can to bring us home.”

Russia has hinted at wanting to swap Ms. Griner for Viktor Bout, a former Soviet military officer who was convicted of offering to sell weapons, including antiaircraft missiles, to federal agents posing as members of the Revolutionary Armed Forces of Colombia.

After Ms. Griner pleaded guilty to drug charges this month, maintaining that she did not intend to break the law, Deputy Foreign Minister Sergei A. Ryabkov of Russia said that the “hype and publicity” surrounding her detention “creates interference in the truest sense of the word.”

In some situations, particularly when the Americans are already well known, the State Department official said public attention could help.

But more often than not, and even when it appears outwardly that negotiations are at a halt, officials are quietly working on the case, he said.