After a shootaround in Memphis during the Western Conference semifinals, Klay Thompson kept talking about having something to prove. He, Stephen Curry and Draymond Green had been through so many different types of playoff battles together with Golden State, and won three championships through it all, but still he felt something was missing.

“I think we still have to prove that we want to go down as some of the greats,” Thompson said. “And the greats have won in multiple decades, and we have yet to win in the 2020s. So it’s right there for us.”

It is no sure thing this year, but the next step in their quest begins Wednesday when they face the Dallas Mavericks in Game 1 of the Western Conference finals.

Dallas and Golden State upset higher-seeded teams in tense conference semifinals series. No. 4-seeded Dallas beat the top-seeded Phoenix Suns by dominating the clinching Game 7. The Mavericks led by 46 points in the second half. No. 3-seeded Golden State won a tightly contested matchup against the second-seeded Memphis Grizzlies in a physical six-game series.

Here is what to expect in the Western Conference finals.

Which players are important to watch?

Curry, Thompson and Green have spent their entire careers with the Warriors and are eyeing a legacy-defining postseason run. Curry made the most 3-pointers in the N.B.A. this season, with 285, even though he missed 18 games. In the fall, he became the league’s career leader in 3-pointers made, passing Ray Allen.

Golden State also features the third-year guard Jordan Poole, who blossomed this season and started in 51 games. He even started a few games ahead of Curry in the playoffs while Curry worked his way back from an injury. Golden State also has forward Andrew Wiggins, who has played better than he often gets credit for. He has been an effective rebounder and important defensive piece for Golden State.

The Mavericks are led by Luka Doncic, who is averaging 31.5 points per game in the playoffs and scored 45 points in Game 1 of Dallas’s series against Phoenix. He closed the series with 27 points in the first half of Game 7 — as many as the whole Suns team had scored. Point guard Jalen Brunson has also had a standout postseason. He is averaging 22.9 points per game in the playoffs, up from his regular-season average of 16.3.

Do these teams have a playoff history?

Quite a notable one.

Golden State’s 2006-7 team is known as the We Believe team in Warriors lore. Led by Baron Davis and Stephen Jackson, it needed a late-season push to make it into the playoffs. There, Golden State met a top-seeded Dallas team that had made it all the way to the N.B.A. finals the previous season, losing to the Miami Heat.

Dallas had reloaded and gone 67-15 during the 2006-7 season, the best record in the league. Dirk Nowitzki won the league’s Most Valuable Player Award. The Mavericks didn’t lose a single game in February. It made what happened next all the more shocking.

In the playoffs, No. 8-seeded Golden State beat Dallas in six games. The magic was short-lived as the Warriors lost their second-round series to the Utah Jazz in five games, but that We Believe team season remains meaningful for fans of Golden State. It was also the last time Golden State faced Dallas in the playoffs.

What has Golden State been doing since its title runs?

After five straight N.B.A. finals appearances, the luck ran out — at least momentarily — starting in 2019.

Thompson and Kevin Durant had major injuries during the 2019 finals against Toronto. Thompson tore his left anterior cruciate ligament, and Durant tore his right Achilles’ tendon, then left for the Nets in free agency. Curry broke his left hand in the fourth game of the 2019-20 season, and played just one more game that season. Without Curry and Thompson, Golden State missed the playoffs.

Then, as Thompson healed from his A.C.L. injury, he tore his right Achilles’ tendon and also missed the 2020-21 season. Golden State was slightly better last season, finishing eighth in the West, but missed the playoffs after losing in the play-in tournament.

While the Warriors waited, they added talented young players like Poole, James Wiseman and Jonathan Kuminga to complement their stars. Wiseman has been out with injuries, but Poole and Wiseman have been important role players. Gary Payton II, who is older than Kuminga, Poole and Wiseman but finally got a stable N.B.A. job this season at age 29, was a pesky defender until he broke his elbow against the Grizzlies in the conference semifinals. Golden State’s two-year absence from the playoffs gave its stars a heightened appreciation for being back this year.

What’s new with the Mavericks?

They have a new coach in Jason Kidd, who played for the Mavericks twice, including after they drafted him second overall in 1994. He had been a head coach in Brooklyn and Milwaukee, spending one year with the Nets and four with the Bucks. Kidd spent two seasons as an assistant coach for the Lakers before Dallas hired him last summer to replace the longtime coach Rick Carlisle.

The Mavericks also shook up their roster this season, trading Kristaps Porzingis to the Wizards for Spencer Dinwiddie and Davis Bertans. It was a clear indication that they were giving the reins of their team to Doncic. Dinwiddie also became an important part of Dallas’s Game 7 win over the Suns, scoring 30 points.

What gives Golden State an edge?

The team is an amalgamation of veterans with playoff experience unmatched among the remaining teams and youngsters who are in the postseason for the first time. That combination is hard to compete against: Curry, Green and Thompson are able to give Golden State’s younger players a crash course in how to win in the playoffs. The young players offer a cushion when the veterans need to recharge.

Not to mention, Curry and Thompson are still playing at All-Star levels now that they’re healthy.

What gives Dallas an edge?

It is tempting to just write “Luka Doncic” and call it a day, but that doesn’t give enough credit to a well-rounded Mavericks team that stifled the Suns defensively in the conference semifinals. Although Dallas’s defensive rating for the season was similar to Golden State’s, the Mavericks closed the year with strong defensive performances.

Stopping Doncic will be a challenge for Golden State, as Dallas’s offense goes almost completely through him. Doncic ranked third in the N.B.A. in points per game this season and fifth in assists per game. He is a generational talent who welcomes the pressure that comes with big moments.