A historic Major League Baseball season is reaching a thrilling climax as teams including the New York Mets and Yankees find themselves embedded in storylines where division titles hang by threads, wild-card berths are up for grabs, and the worst record in baseball history remains in play.

“I’m excited,” the Mets first baseman, Pete Alonso, told reporters at Philadelphia. “We’re playing meaningful baseball. This is what we prepared for a year and now it’s here. Now we’ve got to go do it.”

With a week left in the season, the Mets face a crucial three-game series against the Braves in Atlanta beginning Tuesday. Six games out of a wild-card spot on May 29, the Mets are two games ahead of the Braves and own the second NL wild-card on a tiebreaker over the Arizona Diamondbacks. The Mets (87-69) have the best record in the majors since the end of May, putting them in the thick of the wild-card race along with the San Diego Padres (90-66), the Diamondbacks (87-69), and the Braves (85-71).

“We’ve played excellent baseball for a really long time,” Mr. Alonso, an impending free agent, said. “I think people are going to think of the 2024 Mets with, ‘Oh my God’ or Grimace, but the one word that for me comes to mind is ‘resilient.’ We’ve earned the right to be in this position.”

The Mets have stayed competitive despite losing shortstop Francisco Lindor, who has missed seven straight games because of a sore back and is uncertain when he’ll return. He last played on September 15 after batting .271 with 31 homers, 86 RBI, and 27 stolen bases. He was hitting .307 with 24 homers and 64 RBI in his last 101 games.

The Mets will lean heavily on closer Edwin Diaz, who preserved a 2-1 win over the Philadelphia Phillies on Sunday with the second six-out save of his career and first since August 4, 2022. “It’s big boys time,” the manager of the Mets, Carlos Mendoza, said.

Same applies for the Yankees. The Bronx Bombers need just one win over the Baltimore Orioles in their three-game series that begins Tuesday to clinch the American League East title.

The Yankees, who already have clinched at least a wild-card berth, also have a 2 1/2-game lead over the Cleveland Guardians for the best record in the American League, which would earn home-field advantage through the American League Championship Series.

“Everyone in that room knows what’s at stake and what the mission is and where we’re at in the calendar the opportunity in front of us,” the Yankees manager, Aaron Boone, said. “I think guys are ready to do what we got to do to win ballgames and give ourselves a chance come October.”

The top Yankees slugger, Aaron Judge, has gotten hot at the right time. After going a career-high 16 games without a home run, Mr. Judge smashed four in nine games, including his 55th this season in a 7-4 win at Oakland on Sunday against the A’s.

Meanwhile, the AL wild-card race is a nail bitter, with a surprising contender. The Detroit Tigers have won 11 of their past 14 games to claim the final wild-card spot if the season ended today. The Tigers were 52-57 at the trade deadline and shipped some of their best players for prospects. Somehow, the team got better and the Tigers (82-74) find themselves in a dogfight with the Minnesota Twins (81-75), the Kansas City Royals (82-74), and the Seattle Mariners (80-72) for the final wild-card spot with six games remaining.

Even the Los Angeles Dodgers, riding the historic 50/50 season of Shohei Ohtani, need to close out the San Diego Padres this week to assure themselves of winning the NL West. The Dodgers own a three-game lead over the Padres but face their rivals in a three-game series starting Tuesday at Dodger Stadium. Meanwhile, Mr. Ohtani continues to add to his prolific numbers. The founder and sole member of the 50/50 club now has 53 home runs and 55 stolen bases on the season, his first with the Dodgers.

And then there’s the Chicago White Sox: They matched the 1962 expansion Mets for the worst record in baseball history post-1900 by losing their 120th game Sunday at San Diego. To avoid setting the record for futility, the White Sox will need to win each of their remaining six games against the Los Angeles Angels and the Tigers.