(CNN) Some 75 years ago, on June 6, as US and allied troops were storming the beaches at Normandy, West Point held its commencement ceremony for the Class of 1944 .

As the world commemorated D-Day on Thursday in France, a training accident that killed at least one West Point cadet and injured 19 others and two soldiers focused attention on the US Military Academy, which most Americans might know little about but which has had an outsized influence on US history.

West Point was built as a military base overlooking the Hudson River north of New York City and it was George Washington's headquarters during a portion of the Revolutionary War. It features prominently in Benedict Arnold's betrayal of Washington; the turncoat tried to surrender the base to the British before fleeing to the other side.

Thomas Jefferson signed the legislation that established West Point as the US Military Academy in 1802 with the aim of training engineers, a tradition that carries through today.

The US Military Academy -- the oldest of five such service academies funded by the government to train military leaders -- might be most visible to many Americans as one side in the annual Army-Navy footbll game, but the West Point graduates, known collectively as the " Long Gray Line ," have played pivotal roles in American life.

"The Long Gray Line has never failed us," Gen. Douglas MacArthur told graduates in 1962, before invoking the school's motto. "Were you to do so, a million ghosts in olive drab, in brown khaki, in blue and gray, would rise from their white crosses, thundering those magic words: 'Duty, honor, country.' "

Two presidents were West Point graduates: Dwight D. Eisenhower and Ulysses S. Grant both served two terms after successfully leading US armies in World War II and the Civil War, respectively.

It was Eisenhower who gave the order that allied troops invade Europe through France, launching D-Day.

The former Commander in chief of the Allied forces in Europe (1943) and the future US President General Dwight David "Ike" Eisenhower (1890-1969) poses for a photographer in 1951 at NATO Paris headquarters.

He was also the President who warned on his way out the door of a "military-industrial complex."

Neither Eisenhower nor Grant had distinguished West Point careers, but they are among its most storied graduates.

History does not view all West Pointers so kindly. Their ranks also includes some venerated Confederates whose legacies have recently been under scrutiny, including Robert E. Lee, Stonewall Jackson and Jefferson Davis, who was President of the Confederacy.

Another West Point graduate, retired Gen. Stanley McChrystal, recently wrote thoughtfully about his own reappraisal of Lee's legacy as a man and a leader.

While Eisenhower was in the middle of his class at West Point, MacArthur got highest honors and seemed destined for greatness. He led US forces in the Pacific during World War II and administered postwar Japan with an outsized personality, dark glasses and a corncob pipe.

He was largely responsible for starting the US military engagement in Korea, while Eisenhower, as President, was largely responsible for bringing the US out.

The two can be viewed as a yin and yang of West Point's influence during that crucial time in world history.

Gen. Douglas MacArthur, center, and other U.S. military personnel observe the shelling of Inchon from the U.S.S. Mt. McKinley, on September 15, 1950.

They're far from the only generals who went from West Point to worldwide acclaim. Add Gens. John Pershing, George Patton, David Petraeus, Omar Bradley, McChrystal, Norman Schwarzkopf. The current secretary of state, Mike Pompeo, was the top graduate in the Class of 1986.

The academy's approximately 4,500 students are known as cadets and it is ranked first in US News and World Report's list of Top Public Schools , in part because of its strong engineering programs and in part because it is free of charge. It is one of the most selective schools in the country: Only 10% of applicants are admitted, according to US News . Cadets are paid while they attend, but they owe time to the military as commissioned officers after graduation.

At a time when student debt is of chief concern to college-aged Americans, that might seem like a bargain. On the other hand, the US is embroiled in standoffs around the world, and West Point graduates, like all military officers, have a good chance of being deployed.

The school's website brags to prospective cadets that its alumni include 83 Medal of Honor recipients, 20 astronauts and 93 Rhodes Scholars.

West Point today is primarily meant to train US military leaders, and when Vice President Mike Pence gave the commencement address to the 221st graduating class there in May, it was noted that the academy was graduating its most diverse class in history. More than 5,000 women have graduated since they were first admitted for the Class of 1980.

That's a very small number compared with the nearly 500,000 active-duty service members in the US Army.

Each cadet costs the US government more than $300,000 over four years, which has led some to argue that pulling all officers from ROTC programs at nonmilitary schools would be a better system. There's data that suggests West Point officers do not advance further in the military.

West Point has weathered criticism since its inception. In 1830, Davy Crockett, as a congressman, complained that cadets were "generally the sons of the rich and influential" and were "too delicate, and could not rough it in the army like men differently raised."

32 African American women were with the Class of 2019, the most in the United States Military Academy's history.

Applying to attend can be a difficult process. It includes the requirement of being nominated in one of two categories: congressional (by the vice president, a member of Congress or a senator) or service-connected. There are physical fitness requirements. And freshman cadets must report for duty early in the summer and undergo intensive, miserable-sounding basic training known as Beast Barracks , at which they learn the military lifestyle.

Some of this carries over to the school year, when cadets must wear uniforms and are expected to observe protocols in how they eat and interact. They can and likely will receive demerits and punishments. Hazing is not allowed, but it has been part of the culture. Books have been written about hazing at West Point . There was a congressional inquiry in the early 1900s

The cadets involved in the accident Thursday had likely completed their first year. But they still spend the summer in a variety of trainings, either at West Point or other Army bases.

Not everyone can make it through. Edgar Allan Poe was expelled. Timothy Leary, the LSD guru who encouraged people to "turn on, tune in, drop out," dropped out of West Point.