It's the first time since 2006 that all four top-seeded women reached the semifinals at a Grand Slam tournament.
The Williams sisters overwhelmed their opponents Tuesday with breathtaking displays of power tennis, showing why they have dominated on the grass of the All England Club for most of the past decade.
"We definitely upped our levels of game today," Serena said.
Venus, seeking her third straight Wimbledon title, outhit the 14th-ranked Pole from all parts of the court and proved again that she is the dominant female player on grass.
"Do I feel invincible?" Venus said. "I'd like to say yes, but I really do work at it."
Venus had her left leg taped up again but showed no weakness at all as she ripped 29 winners -- compared to six for Radwanska -- in a match that lasted just 68 minutes on a sunbaked Court 1.
"I can't complain," Venus said. "I'm in the semifinals of Wimbledon, right where I want to be. I just need to take another step forward."
With Venus looking on from the guest box, Serena swept through the first set against the eighth-ranked Azarenka in 26 minutes. After being broken to go down 3-2 in the second, she won four straight games and held serve at love to finish the match in commanding fashion. Serena had nine aces and 26 winners, with only seven unforced errors.
Azarenka had beaten Serena in straight sets in their last match in the final at Key Biscayne, Fla., in April.
"I really wanted to do well today," Serena said. "I didn't do well the last time we played. I was not feeling great. I felt like I really wanted to show up today."
Asked whether she also felt unbeatable at Wimbledon, Serena said: "I don't feel invincible, but I definitely should have the same attitude. I'm going to try to feel that way, too."
Only once in the last nine years has there been a Wimbledon women's final that didn't feature at least one of the Williams sisters. The sisters were the only two Grand Slam winners in the women's quarterfinals -- Serena has 10 major titles and Venus seven.
The sisters have met in three Wimbledon finals, including last year. Serena has won two of the three, in 2002 and '03. They are 10-10 in career meetings.
"I would love it to be a Williams final, and so would she," Venus said. "That would be great."
The sisters' father, Richard Williams, said he is certain his daughters will be in the final again.
"I think they are both playing super well," he said. "They're playing the Williams way. And when you're playing the Williams way, it's very difficult for anyone to touch you."
Venus is trying to become the first woman since Steffi Graf in 1991-93 to win three Wimbledon titles in a row.
Venus raced to a 5-0 lead against Radwanska and finished off the first set with back-to-back aces. She dropped only two of 18 points on serve in the set.
"That first set for me was almost perfect," Venus said.
Safina, who has risen to No. 1 in the world despite never having won a Grand Slam title, struggled against the 19-year-old Lisicki. The Russian had to come from behind after double-faulting to lose the first-set tiebreak, smashing her racket to the turf and drawing a warning from the chair umpire.
"I was Santa Claus on the court, serving so many double-faults," Safina said.
Safina was down 3-2 on serve in the second set but got the one break in the seventh game to force a third set. The 41st-ranked Lisicki received treatment on her right calf after going down 4-1 in the third. In the next game, Safina was up 40-0 before serving three straight double-faults. She still managed to hold and then broke for the match.
"I was tough mentally, that was the key today," Safina said.
Dementieva, meanwhile, grabbed a 5-0 lead in the first set against the 43rd-ranked Schiavone and converted both of her break points in the second to seal the win in 66 minutes.
Dementieva also reached the Wimbledon semifinals last year. She is still looking for her first major title after being runner-up at both the French Open and U.S. Open in 2004.
Temperatures topped 90 degrees on Tuesday, with no need to close the roof on Centre Court.
Medical officials on site said they treated more than 130 people, mostly for heat-related problems. One person was taken to a hospital.