"Mission 33" -- the long-awaited 33rd career win -- has been a rallying cry for fans of the Spaniard, now enjoying a revival with Aston Martin.
His 32nd win was with Ferrari in May 2013 and Sunday's race could be emotional.
If the heart beats for Alonso, with even Verstappen admitting in Monaco last weekend that he would love to see his fellow double champion win again, the head points to Red Bull's runaway championship leader.
Red Bull have won every race this season and the Dutchman who now has the champion's number one on his car, has taken four of the six.
Mexican teammate Sergio Perez has won the other two but is 39 points adrift after failing to score in Monaco.
The big ongoing questions are whether Red Bull can do the unprecedented and win all 22 races this season, whether Verstappen will take more than last year's 15 victories and where the third title might be won.
Some would add "Can Perez fight back?" but history offers little encouragement once Verstappen has got going.
"Monaco was a disaster for me. Everything that could have gone wrong went wrong. So this weekend is all about starting again," said Perez.
Verstappen won in Spain in May 2022, when the race was the sixth round, to take the overall championship lead and he has not relinquished it since.
For Alonso, runner-up in Monaco after four third places in the other five races, another podium finish has to be the target.
"We have scored lots of third places, a second place in Monaco and the next one we need is the top step. To do this we have to maximise every part of our weekend and capitalise on any opportunities that may come our way," he said.
He could face tougher opposition than last weekend with compatriot Carlos Sainz also eyeing a home win and Ferrari hoping upgrades will put the Italian team closer to the front. Sainz finished fourth last year, his best home result yet.
"In Monaco we couldn’t show the real potential of our car, but the race in Barcelona will provide a clearer picture," said team boss Fred Vasseur.
Mercedes also have upgrades that will be watched much more intently after a low-speed debut in Monaco that was hardly indicative.
The Barcelona layout has returned to the one used until 2006, and seven-time world champion Lewis Hamilton has won there a record-equalling six times.
"Barcelona is probably the best test circuit we could ask for in order to learn more about our package. I'm looking forward to seeing how the car reacts," said Hamilton.
