The history of baseball is wide and vast, but in many ways, you can encompass a large percentage of it in two of the premier teams of today: The Yankees and Red Sox. Responsible for a stunning 36 World Series championships, their rivalry transcends more than just the enmity between the teams; if anything, the rest of baseball should have a rivalry with them.

And, inevitably, many of baseball’s greatest players wore the uniform of one of these teams at some point. Some are all-time greats who only briefly played for either team: Rickey Henderson, Ivan Rodriguez, Randy Johnson, etc. But the true all-timers are the ones who made their careers with either team, players who are as lodged in Yankees and Red Sox history as they are in baseball history itself. So, today, as the two teams prepare to play their first series of the season in a year in which they will play the first ever Major League regular-season series in London, we look at the 20 best Yankees and Red Sox players of all time.

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Note: We’re excluding players like Henderson and Johnson here. You don’t have to have played exclusively for either team, but you do have to have played mostly for them.

1. Babe Ruth

The Bambino is hardly a difficult choice at No. 1, either on this list or any all-time list. Not only is he the most dominant baseball player who ever lived, he also won seven World Series: Four with the Yankees and three with the Red Sox. Nearly 90 years after he retired, he’s still the most famous baseball player who ever lived.

2. Ted Williams

The Splendid Splinter's obsessiveness and natural skill allowed him to square up a baseball better than anyone on the planet. He won the Triple Crown in 1942, went to fight in World War II for three years, and then won another Triple Crown the year after he returned. He remains the last player ever to hit over .400 in a season.

3. Mickey Mantle

Gifted with talents that seemed carved out of the mold of the gods themselves, Mantle was as indestructible a pure baseball talent as America had ever produced: He looked like, and played like, the platonic ideal of a baseball player. His 1956 American League MVP season is one of the greatest individual seasons ever.

4. Lou Gehrig

The Iron Horse, Gehrig was Ruth’s less gregarious fellow superstar on one of the greatest baseball teams in history. His “Luckiest Man on the Face of the Earth” speech, and his tragic death from the disease that now bears his name, immortalized him in popular culture, but as a baseball player, he was as close to Ruth’s equal as anyone of their era.

5. Joe DiMaggio

The Yankee Clipper, DiMaggio was the walking embodiment of his time, a seemingly flawless American icon who married Marilyn Monroe and was the subject of songwriters decades after his death. “Joltin’ Joe” is the baseball player every baseball player wishes they were. Mantle himself once said, “Heroes are people who are all good with no bad in them. That’s the way I always saw Joe DiMaggio."

6. Cy Young

When they name the award for the best pitcher of the year after you, well, you’ve done something right. Young also owns the one baseball record that will never be broken: 511 career wins, a number so high that it’s more games than some Hall of Fame pitchers have even appeared in.

7. Yogi Berra

Baseball’s great lopsided philosopher, Berra has become such a quotable, lovable figure in Americana -- his Zen-like proverbs of odd wisdom (“It ain't over till it’s over,” “Nobody goes there anymore, it’s too crowded”) will outlive us all -- that it’s not always appreciated just how brilliant of a baseball player he was. He won three MVP Awards and, counting his time as a coach, he won a stunning 13 World Series. If you don’t know where you are going, you’ll end up someplace else.

8. Mariano Rivera

Baseball’s greatest closer, and considering how much the role of closer might be changing, he might even go down as the last one in the traditional sense. The first player ever to be unanimously elected to the Baseball Hall of Fame, Rivera is one of the only players on this list about whom the opposing side never had a bad word to say.

9. Tris Speaker

Speaker spent only the first half of his career with the Red Sox, and his best seasons might have been with Cleveland. But Speaker is one of the most underrated players in baseball history, particularly his defense, which was so good it earned him the nickname “Where Flying Things Go To Die,” a nickname as fantastic as it is unwieldy.

10. Lefty Grove

Famously mild-mannered, Grove was so quiet and reserved that one historian said he looked like “the professor of the pitching department.” He also happens to be thought of by many to be the greatest left-handed pitcher of all time (hence the nickname).

11. Roger Clemens

One of the few players to excel for both the Red Sox and the Yankees, he was the dominant phenom in Boston before becoming the ornery veteran cuss in the The Bronx at the turn of the century. He remains one of baseball’s most controversial figures, but he won seven Cy Young Awards and was firing 95-mph fastballs to the very end of his 24-year career.

12. Alex Rodriguez

The fact that A-Rod is above Derek Jeter on this list -- not to mention so many other beloved luminaries -- may have just compelled you to fling your device across the room and against the wall. But Rodriguez, for all his faults and foibles, was a truly transcendent baseball talent. He didn’t always make things easier for himself off the field, but if you can gloss over the distractions better than he did, his achievements are impossible to ignore.

13. Carl Yastrzemski

Yaz retired at the age of 44 after 23 seasons with the Red Sox; he had spent more years on Earth playing for the team than he hadn’t. He made 18 All-Star Games, has played the second-most games in baseball history and has the third-most at-bats: For two and a half decades, he was Boston baseball.

14. Pedro Martinez

A truly breathtaking pitcher to watch, Pedro was a live wire with excessive electricity running through it, a guy who, at his peak, displayed an absolute mastery of the mound. A whole new age of Red Sox baseball was represented by Pedro at Fenway, dazzling and baffling hitters: His legendary appearance at the 1999 All-Star Game secured his place in Fenway lore forever.

15. Derek Jeter

As universally adored as any baseball player of his time -- no small feat, considering how fractious his era was -- Jeter was a throwback to the kings of DiMaggio and Mantle. He will forever be the Captain in the Bronx, and the model of how to purport yourself as a superstar athlete in the modern age.

16. David Ortiz

Boston’s irascible, occasionally profane, always delightful answer to Jeter’s stoicism, Big Papi may be the greatest postseason hitter since the playoffs expanded in 1995. And in the wake of the Boston Marathon bombing in 2013, he became the city’s resilient, unbreakable voice.

17. Bill Dickey

Bob Feller said Dickey was the best catcher he ever saw, and Berra himself said all he knew about catching, he learned from Dickey.

18. Whitey Ford

A Yankees lifer, Ford was famously reliable, particularly in the postseason. He pitched in a stunning 11 World Series, winning six of them and earning the 1961 Series MVP.

19. Wade Boggs

The notoriously superstitious Boggs, who ate chicken before every single game he ever played, was a lifetime .328 hitter, though, much to the chagrin of Red Sox fans, he won his one title with the Yankees after a decade-plus in Boston.

20. Jim Rice

One of the most feared sluggers of his time and a Red Sox fan favorite for his entire 16-year career, it took him 15 years to finally reach the Hall of Fame … but reach it he did.