He’s young and handsome and boasts a family tree with six centuries of kings and queens. She’s smart and glamorous and doesn’t have a drop of blue blood. They are the very model of a modern royal couple.

William and Kate?

No, King Felipe VI and Queen Letizia of Spain, who arrive in Washington this week for their first official visit — without the frenzied media mob that follows the British monarchy. There are no breathless morning television countdowns, no stakeouts for their trips to Mount Vernon or the White House. They could walk the streets of Georgetown, where he attended graduate school, without turning a single head.

But Spain’s new king and queen are sexier, slightly scandalous, and more interesting than the squeaky-clean Duke and Duchess of Cambridge. Felipe was the cherished royal son expected to marry a nice Catholic princess — until he defied his parents for a love match. Letizia is the first Spanish commoner to become queen, a feat even more remarkable when you realize that she was a celebrity journalist with an ex-husband and a live-in boyfriend before meeting her prince.

The couple will meet with President Obama and Senate leaders on Tuesday (which happens to be the queen’s 43rd birthday), open an American-Spanish scientific conference at Georgetown University, meet with American chief executives who do business in Spain, and head to Florida to celebrate the 450th anniversary of St. Augustine. They’re the standard feel-good duties of 21st-century royalty: pretty pictures, business development, warm words about friendship and cultural ties.

The visit comes after a rocky first year on the throne: After 39 years as king, Felipe’s father, Juan Carlos, abdicated last year amid questions of royal excess and infidelity. One of his sisters is about to go on trial for tax fraud. And his country is crawling back from a crippling economic crisis.

The question is whether these two mortals — one a descendant of Ferdinand and Isabella, the other the granddaughter of a taxi driver — can save the fragile Spanish monarchy.

British biographer Andrew Morton, who knows a thing or three about modern royals, says it comes down to one woman: “The weight of the future rests on the slender shoulders of Letizia.”

Letizia and Felipe on their wedding day in 2004. (Christophe Simon/Agence France-Presse via Getty Images)

Felipe Juan Pablo Alfonso de Todos los Santos de Borbón y Grecia was born in Madrid on Jan. 30, 1968, the third child and only son of King Juan Carlos I and Queen Sofia. Because Spain still adheres to the male line of succession, Felipe became crown prince and heir to the throne.

He was always a serious kid who embraced his future role with a laserlike focus: military training in the army, navy and air force, where he became a helicopter pilot; a law degree in Madrid; a master’s in international relations from Georgetown University; speaker of Spanish, French and English. From the age of 22, he began the lifelong job of traveling throughout Spain and Latin America soaking up all things Spanish. In 1992, the 6-foot-6 sports nut enjoyed one of the real perks of being prince: a spot on the Spanish sailing team at the Barcelona Olympics, where he carried his country’s flag at the opening ceremony.

He only strayed from the predictable path when it came to women. He had no interest in a princess bride, and his parents vetoed two serious girlfriends as unsuitable marriage material. One was a Spanish socialite with a family drug problem, the other a Norwegian underwear model. Then he met Letizia Ortiz Rocasolano.

Born in 1972, she was the daughter of a journalist and a nurse, a middle-class girl with high-class ambition. She married her high school literature teacher when she was 25, a union that lasted less than a year. The beautiful brunette quickly rose in her broadcasting career, reporting for Bloomberg News, CNN and Television España. She was named the best Spanish journalist under the age of 30 and landed an evening anchor spot — and moved in with her sports-reporter boyfriend. Everyone in Spain knew her name.

Then, while reporting on an oil spill off the Spanish coast in late 2002, she ran into Felipe. The two met earlier that year at a dinner party, but this time he asked her for a date. They kept the courtship under the radar and announced their engagement a year later. Instead of a prim dress, Letizia wore a sexy white pantsuit to meet reporters and created a stir when she chided, “Let me finish,” after Felipe interrupted her.

His parents were opposed to the match. It wasn’t just that Letizia had no pedigree; other royals in Europe (Denmark, Sweden, the Netherlands, Norway, Monaco and, of course, Britain) were marrying commoners left and right. But she was “the very antithesis” of a classic Spanish queen — divorced, worldly, opinionated and a celebrity journalist, says Morton, author of “Ladies of Spain,” a tell-all about the Spanish royal family. Juan Carlos called his future daughter-in-law “the enemy within,” he says. “He was very hostile to the idea.”

Felipe won that argument, and the two married in May 2004. Letizia’s first marriage was officially erased: Because she wed in a civil ceremony, that union was not recognized by the Roman Catholic Church and she could marry the prince without getting an annulment. The wedding was watched by 25 million people in Spain, and the bride officially became a princess.

It is, by all accounts, a happy marriage. The couple have two daughters: Infanta (princess) Leonor, 9, and Infanta Sofia, 8. Felipe quickly embraced his roles as husband and father and looks happiest in informal photos with his family.

But from the beginning, all eyes have been fixed on Letizia. There was constant gossip about her nose job (for respiratory problems, says the palace), her perfect figure, her designer clothes, an unbending perfectionism, her royal duties and other outrages real or imagined — especially from Spain’s old aristocrats, who resent that Felipe never once looked in their direction before he married a middle-class commoner.

Felipe and Letizia with their daughters, Leonor, right, and Sofia, at the Marivent Palace on Mallorca last year. (Jaime Reina/Agence France-Presse via Getty Images)

Last week, Queen Elizabeth II became Britain’s longest-serving monarch — an accomplishment not at all certain 20 years ago, after separations, divorces and public calls for the abolition of the institution. Now the Spanish monarchy is on shaky ground, a fate few would have predicted in the heyday of King Juan Carlos I.

In 1931, Alfonso XIII left Spain when the Second Republic was proclaimed, which looked like the end for the Spanish royal line. Gen. Francisco Franco, who became dictator in 1939, named Alfonso’s grandson, Juan Carlos, his successor because he believed that the prince would follow in his footsteps. Franco miscalculated: After the general’s death in 1975, the new king called for democratic elections and prevented a military coup in 1981, which brought him enormous personal popularity. Even socialists embraced the new king, which led to the popular saying, “I’m not a monarchist. I’m a Juancarlist.”

“The monarchy has played a very important role, and still plays an important role, in Spain,” says Ramon Gil-Casares, Spain’s ambassador to the United States. “The monarchy got us out of dictatorship, gave us stability. People know that and recognize themselves in the king and queen.”

Juan Carlos was handsome, charming and one of the last old-school kings: He married a Greek princess and had three children. He loves women, wine and the finer things of life. That proved to be a problem in 2012, when the 74-year-old monarch went on an unannounced elephant hunt in Botswana with a German socialite whom tabloids identified as his longtime mistress. The trip came to light when he broke his hip and had to be flown out of the country; Spanish citizens, barely scraping by in one of the country’s worst recessions, were furious at the excess and the droit du seigneur mentality.

The royal family was already struggling with a scandal closer to home: Princess Cristina and her husband, Iñaki Urdangarin, were accused of taking millions of charitable donations for private use. The case is ongoing, and the princess, the first member of the Spanish royal family to be indicted, faces more than a decade in prison if convicted of tax fraud and money laundering.

The hunting trip was the last straw. It was open season on the royal family, and everyone was fair game. Juan Carlos was urged to abdicate to save the throne. He stepped down last year, citing health issues and his son’s readiness to assume the title.

There was no fancy coronation, just a ceremony in front of the parliament on June 19, 2014, where Felipe, with Letizia and his daughters at his side, took the oath of office and the formal title of His Majesty King Felipe VI of Bourbon and Greece. The 18th-century Spanish crown was displayed but not placed on his head, no foreign royals were invited, and there was an afternoon reception for 2,000 guests with tapas instead of a lavish banquet. Juan Carlos and Cristina did not attend.

In his first address as king, Felipe tried to reassure the politicians and public that things had changed: “These are my convictions about the Crown, which from today I shall embody: a renewed monarchy for new times. And I undertake my task with energy, with enthusiasm and with the open and innovative spirit that has inspired the men and women of my generation.”

“I always say to my American friends, ‘We measure our history by reigns,’ ” says Gil-Casares, the Spanish ambassador. “So this is the Spain of Felipe VI.’ ”

King Juan Carlos and Felipe attend a military ceremony outside Madrid in 2014. (Daniel Ochoa De Olza/AP)

“When King Juan Carlos abdicated, the monarchy was in bad shape,” says Marc Bassets, U.S. bureau chief of El País, one of Spain’s largest newspapers. The royal family’s approval ratings had slumped to 30 percent. “Monarchs have to win the hearts of Spaniards,” says Bassets. “The monarchy cannot take anything for granted. Kings have to earn their salary and their roles.”

Intelligent, shy, cautious, Felipe may be the right king for Spain right now. “He doesn’t have his father’s charisma, but he makes up for that by working really hard,” says Morton. In his first year on the throne, Felipe cut his own salary by 20 percent (the king gets 234,204 euros a year, about $265,000 ) and posted all the royal salaries and expenditures online for anyone to see. The royal family, staff and residences cost Spanish taxpayers about $9 million annually. (Britain’s royals, by contrast, officially cost taxpayers $58 million per year, although critics claim that the actual number is 10 times that.)

Felipe also banned members of the royal family from working for private companies or accepting expensive gifts, stripped his sister of her title of duchess and her duties, and has promised that no one is above the law. “Public office must not be a means to profit or becoming rich,” he said in his first Christmas address to the nation. “We must not hesitate to cut corruption at its roots.”

Last year, Felipe’s personal approval ratings were at 62 percent; a new poll puts him at 81 percent (and the queen at a healthy 74 percent). Even the leader of a new leftist party praised the king on his first anniversary — which is critical but rarely discussed, says Morton: “Monarchies do not fall or rise by popular opinion. It’s politicians who decide. In Spain, there’s no appetite among the political class to abolish” the throne.

Besides, Spain — still struggling with more than 20 percent unemployment and an uncertain economy — is less concerned with the monarchy right now than with the growing secession movement in the northeastern region of Catalonia, where more than a million people marched through the streets of Barcelona last week calling for independence. The wealthy, educated taxpayers are balking at footing the bill for the poorer regions of the country; local elections at the end of September will determine how serious the threat really is. The king is officially above the fray but speaks Catalan and has visited the region several times in the past year.

So, for the moment, the Spanish crown is (relatively) secure — as long as Felipe and Letizia live happily ever after. “They must stay together for the monarchy,” says Morton. “They’re hanging on by their fingertips.”