BOSTON -- The rivalry between the Boston Red Sox and the New York Yankees is considered one of the greatest in all of sports.

It's built on incredible moments, amazing comebacks, plenty of bench-clearing brawls, and memorable triumphs and heartbreak. Both sides have experienced it all. This rivalry was at its peak during the 2003 and 2004 seasons.

During Game 3 of the 2003 ALCS, Red Sox pitcher Pedro Martinez hit the Yankees' Karim Garcia in the top of the fourth inning at Fenway Park. The benches cleared, but order was quickly restored. In the bottom of the inning, Yankees pitcher Roger Clemens delivered a pitch high and inside on Red Sox hitter Manny Ramirez.

The benches and bullpens emptied again, only this time punches were thrown. The melee escalated when Martinez grabbed Yankees coach Don Zimmer by the head and tossed him to the ground.

The Yankees eventually won that series on Aaron Boone's walk-off home run in the bottom of the 11th inning of Game 7 at Yankee Stadium.

In 2004, another epic chapter was written in the history books. On July 24 at Fenway Park, Red Sox pitcher Bronson Arroyo drilled Yankees cleanup hitter Alex Rodriguez with a pitch in the top of the third inning. Rodriguez had words with Arroyo, before Red Sox captain and veteran catcher Jason Varitek stepped in and shoved his mitt into A-Rod's face, inciting another bench-clearing brawl.

“I knew it would never get any better than that,” Arroyo said in a recent phone interview. “I was 27-years-old and I was seasoned enough in the big leagues where I didn’t feel totally uncomfortable, but I was still young in my career. I knew it was never going to be any better than playing against those guys 19 times a year. It felt like a playoff game every time.

"Things like that dramatize it even more and that was one year removed from the whole Don Zimmer and Pedro Martinez fight, so it was like a heavyweight boxing match all the time, the electricity of a Mike Tyson fight all the time, because you never knew what was going to happen. It was definitely fun to be just in the place, much less in uniform. It was just high drama all the time.”

In October of that season, the Yankees held a 3-0 series lead on the Red Sox in the ALCS, but Boston mounted a historic comeback to win in seven games, before sweeping the St. Louis Cardinals for the Red Sox's first World Series title in 86 years.

There's been plenty more to add to this rivalry since the '04 season, but the fisticuffs subsided.

In August 2013, Rodriguez was able to play after he appealed a suspension for his involvement in the Biogenesis scandal. This did not sit well with many players in the majors, including most everyone on Boston's pitching staff. So, on Rodriguez's first trip to Fenway Park after his appeal, Red Sox pitcher Ryan Dempster drilled Rodriguez with a fastball.

The benches and bullpens emptied, but no punches were thrown.

This season, with Rodriguez serving a season-long suspension, the rivalry seems a bit different. Red Sox veteran DH David Ortiz believes he knows why.

"People right now still question a lot if the rivalry's still going on just because they're not seeing [fights]," he said. "What people need to understand is that right now there are so many rules and so many suspensions that in case something happens with a guy like myself, and I decide to charge a pitcher, I already know I'm going to miss five games at least, and if I miss five games out of that lineup it's going to hurt us.

"Everybody's trying to stay away from that. MLB is trying to keep everybody away from that. MLB has been doing an unbelievable job when it comes down to sending the right message to the fans and there's so many big suspensions because of that. Plus, another thing I believe, you know how pitchers back then used to get mad and angry when you take them deep, and next thing you know they were hitting somebody on purpose, but that's not part of the game anymore, because you know the minute [MLB] finds out that you hit somebody on purpose you're going to have to pay a fine and be suspended, too. So, there's a lot of different things going on right now compared to what the game was 10 or 11 years ago, and that has confused the fans when it comes down to the rival thing. I believe the fans need to pay attention to that a little more."