A Cuban gives the thumbs up from his balcony decorated with the US and Cuban flags in Havana, on January 16, 2015. The United States will ease travel and trade restrictions with Cuba on Friday, marking the first concrete steps towards restoring normal ties with the Cold War-era foe since announcing a historic rapprochement. AFP PHOTO/YAMIL Lage (Photo credit should read YAMIL LAGE/AFP/Getty Images)
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A Cuban gives the thumbs up from his balcony decorated with the US and Cuban flags in Havana, on January 16, 2015. The United States will ease travel and trade restrictions with Cuba on Friday, marking the first concrete steps towards restoring normal ties with the Cold War-era foe since announcing a historic rapprochement. AFP PHOTO/YAMIL Lage (Photo credit should read YAMIL LAGE/AFP/Getty Images)
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(CNN) —  

Cuba was for years the “Red Menace” at the very gates of the U.S.A.

Relations across the Florida Straits turned so bad, that the two countries pushed the entire world to the brink of nuclear war.

Exploding cigars to blow up Cuba’s rebel leader Fidel Castro or toxic potions to make his trademark beard fall out were just two of hundreds of shadowy CIA plots to thwart the Communist Revolution.

U.S. congressional delegation travels to Cuba

But the Cold War between the U.S. and Cuba will begin to seriously thaw this week after more than half a century.

President Barack Obama is sending the highest-level U.S. delegation in decades to the island this week in a controversial bid to “normalize” ties between the two former arch foes.

Spearheading the U.S. diplomatic mission, Roberta Jacobson, assistant secretary of state for Western Hemisphere affairs – she deals with Latin America and Cuba.

Jacobson is scheduled to touch down in Havana this Wednesday.

By the time she arrives, her deputy, Alex Lee, will already be hard at work meeting Cuban officials at the state-run Conventions Palace.

Lee and his team are charged with discussing bilateral migration issues.

To make business easier, U.S. diplomatic sources tell CNN, the U.S and Cuban teams are separating the orders of business.

Cuba’s money makers expect good times as Obama eases restrictions

On Wednesday, Lee will discuss with Cuban officials including the number and types of visas the U.S. offers to Cubans wishing to visit or go live in the United States.

One of the reasons that is so important is that over the decades, thousands of Cubans have left the island either legally or covertly – sometimes in perilous homemade boats or rafts.

On Thursday, Jacobson’s team will meet a Cuban delegation led by her counterpart, Josefina Vidal, the director of the North American Division of Cuba’s foreign relations ministry. Their role is to explore ways to launch normal diplomatic and commercial relations.

There is clearly a lot of work to be done, and this week’s negotiations could chart the path forward for a larger agreement on normalizing relations.

In a conference call with reporters on Monday, a senior State Department official expressed measured optimism about the talks, but noted that much would depend on the willingness of the Cuban government to engage the U.S. on a broad range of issues.

“Certainly in this conversation, we’re able to get on the table all of the things that we are interested in, and all of the things the Cuban government is interested in, so that we know the parameters within which we’re working,” the official said, adding that the U.S. delegation does not expect to close every issue of contention in these talks alone.

Asked whether there might soon be an opportunity for the secretary of state to meet with his Cuban counterparts, the official was hardly dismissive.

“We would see the secretary’s visit down to Cuba as something that would take place in the future,” the official said, adding that such a trip would depend largely on how these and other upcoming diplomatic talks play out.

President Dwight Eisenhower broke off relations with Cuba and shut down the embassy in January 1961.

Two years earlier, leftist rebels led by Fidel Castro and Che Guevara, among others, swept to power ousting Gen. Fulgencio Batista, the dictator backed by the U.S. government and by the U.S. mafia which ran lucrative prostitution and gambling rackets on the island.

Cuba progressively allied itself with the Soviet Union. In April 1961, Kennedy launched the botched Bay of Pigs Invasion.

And in 1962, as the Soviet Union deployed nuclear missiles to Cuba and pointed them at the U.S., the world lurched toward atomic Armageddon in what became known as the Cuban Missile Crisis.

Down the years, the Cuban government backed leftist and Communist regimes and uprisings in Latin America and Africa.

That earned the island a spot on a U.S. blacklist known as the “state sponsors of terrorism” – a dubious classification it still shares with Syria, Sudan and Iran.

Obama’s Cuba details revealed

In later years Cuban-U.S. relations were marked by successive crises sparked by refugees trying to get out of Cuba and cross the Florida Straits in unseaworthy craft.

The meetings scheduled between the U.S. and Cuban delegations this week in Havana are likely to achieve “baby steps” on a much longer road to normalization, U.S. diplomats have told CNN.

One of the practical issues on the table will be the measures needed to convert the U.S. Interests Section – one of the largest diplomatic missions in terms of staff on the island with more than 50 U.S. citizens, including 10 marines who act as guards – into a full embassy. Cuba will be looking to do likewise with its mission in Washington.

The two sides are expected to discuss matters such as staffing numbers and the restriction currently placed on U.S. diplomats that forbids them traveling more than 25 miles from the interests section.

Secretary of State John Kerry has already begun his review about whether to remove Cuba from the state sponsors of terrorism list, U.S. diplomatic sources told CNN.

A senior State Department official told reporters the department expects to complete that review quickly, possibly well ahead of the six month deadline set by the President.

These discussions are the first since Obama last month announced two nations would move towards normalization of relations after decades of a U.S. embargo against the communist nation.

As part of that move, the U.S. relaxed some of the travel restrictions meaning more Americans can visit the island nation. That easing came into effect this weekend.

Previously U.S. citizens had to seek a license from the Treasury Department to go there so now they don’t so long as the travel meets one of a dozen criteria.

While travel restrictions are only now being loosened, already people are visiting Cuba from the U.S. in greater numbers. Last year, 100,000 U.S. citizens visited Cuba on “people-to-people” cultural travel, and some 400,000 Cubans living in the U.S. made trips back to the island.

There was also some easing of commercial rules – Americans can use credit cards while there, and they can bring back $400 worth of Cuban goods and $100 of tobacco or alcohol products.

Cuba releases 53 political prisoners

As part of the talks that led to the normalization announcement last month, Cuba agreed to release 53 political prisoners, but that became controversial as U.S. officials refused to identify them or to say when they would be freed. Last week the State Department announced Cuba had, in fact, freed all of those prisoners.

In addition to talks about opening embassies and re-establishing diplomatic ties, the two governments are also expected to talk about human rights and further commerce.

On migration matters, Havana is especially upset over the U.S. law – the so-called “wet foot-dry foot law” – which allows Cubans citizenship for those who reach American soil. Cuban officials argue the law encourages Cubans to take the dangerous – often fatal – journey across the straits of Florida. It has been widely rumored that that legislation, seen as giving preferential migration status to Cubans, could be revoked.

But U.S. diplomatic sources in Havana told CNN the issue was “not being put on the table by us.”

Several American airlines have expressed interest in starting flights to Havana as soon as the two governments hammer out an agreement authorizing them.

And according to the office of New York Gov. Andrew Cuomo, the governor plans on leading a trade mission to Cuba “in the coming term.”

This weekend, a separate U.S. delegation – led by Democratic Sen. Patrick Leahy and including five other congressmen – is in Cuba. This visit has no direct relationship to Jacobson’s delegation.

CNN’s Kevin Bohn and Laura Koran contributed to this report.