When Brock Lesnar made his way to WWE's main roster in 2002, it didn't take him long to capture the top title. Lesnar defeated The Rock in the main event of SummerSlam to win the Undisputed WWE Title. Immediately after, The Undertaker went on to feud with "The Next Big Thing".
This resulted in Brock Lesnar destroying The Deadman inside Hell in a Cell at No Mercy 20, leaving him in a bloody mess. The duo went on to have another rivalry in 2003, with Lesnar coming out on top again.
Mark Calaway attended UFC 121 with his wife, Michelle McCool, and was giving an interview soon after Lesnar lost his match to Cain Velasquez. Calaway's interview got interrupted in between, when he saw Brock Lesnar making his way past him.
Undertaker stopped for a second, looked at Lesnar, and uttered the words, "You wanna do it?" forcing Brock to stare at the behemoth for a split second. This didn't end up going anywhere as Lesnar chose to leave the spot almost immediately.
In an interview with UFC's Ariel Helwani, Lesnar stated that he had real-life beef with The Undertaker. Brock added that Taker must've confronted him after his loss at UFC because he was a huge name outside WWE, and the WWE guys couldn't digest that fact.
The duo must've settled their differences somewhere down the line, as Brock Lesnar went on to defeat The Undertaker at WrestleMania 30, breaking his 'Mania streak. Apparently, Lesnar didn't want to break the famed streak, but Vince McMahon convinced him to do so, and The former UFC Champion even went on to thank The Phenom seconds after his win at The Show of Shows.