text: Konta continued her remarkable run with a 6-4 6-1 win over China's Zhang Shuai in the quarter-finals and next faces German seventh seed Angelique Kerber.
  Media playback is not supported on this device
  Fellow Briton Murray saw off Spain's David Ferrer 6-3 6-7 (5-7) 6-2 6-3 to reach his sixth Melbourne semi-final.
  The Scot, seeded second, will play Canada's Milos Raonic on Friday.
  Raonic, a Wimbledon semi-finalist in 2014, beat Frenchman Gael Monfils 6-3 3-6 6-3 6-4.
  Konta and Murray have matched the achievement of semi-finalist Sue Barker and runner-up John Lloyd, who both reached the last four at the Australian Open 39 years ago.
  Murray, 28, won a gruelling quarter-final against eighth seed Ferrer that lasted three hours and 49 minutes.
  Konta, ranked 47th, is the first British woman to reach a Grand Slam semi-final since Jo Durie made the US Open last four in 1983.
  Media playback is not supported on this device
  "I'm just so happy that I'm enjoying what I'm doing," said Konta after her straight-set win over Zhang. "That is me living my dream."
  Her achievements so far have guaranteed her prize money of at least £370,000 and are likely to secure her a place in the world's top 30.
  "When I was a little girl, I dreamt of winning grand slams and being number one in the world," she added. "That dream stays the same, I think, as long as you're doing the career that you're on."
  Konta said she "just wanted to come out and play the best level" she could against Zhang, who was also in uncharted waters.
  The British number one saw off the Chinese qualifier, ranked 133rd in the world, in one hour and 22 minutes.
  Konta began confidently, breaking twice and serving superbly as she moved 5-2 clear before overcoming some nerves and a resurgent opponent to clinch the set.
  After saving a break point that would have made it 5-5 and then converting her sixth set point, the confidence returned and Konta again earned a double-break lead in the second set.
  With a semi-final place there for the taking, Konta saw two match points slip by but converted the third thanks to a net cord.
  "To be honest, I was taking it a match at a time," said Konta. "She definitely didn't make it easy for me.
  "Every time I was ahead, she was constantly there. I'm not proud of the net cord, but I'm happy I was able to fight every point."
  A Grand Slam final appearance is now a real possibility, arguably more so after Kerber's surprise win over the in-form Victoria Azarenka.
  Kerber and Konta will meet for the first time in Thursday's second semi-final at around 04:30 GMT.
  Murray is through to his 18th Grand Slam semi-final, bringing him level with Boris Becker, having dropped just two sets in five matches.
  The former Wimbledon and US Open champion was made to work hard by Ferrer, but Murray proved the stronger in the third and fourth sets.
  A three-set win looked possible after he took the opener and fought back from 4-1 down in the second to earn two break points at 4-4.
  Ferrer, 33, showed his famous battling qualities by digging in and forcing a tie-break, which he would win to draw level, prompting Murray to berate himself and talk to those in his player box.
  The Scot was understandably irritated but gathered himself sufficiently to break for a 3-1 lead in the third, at which point the roof was brought across with thunderstorms forecast.
  Murray saved a break point on the resumption, but broke once again to take a grip on the contest and moved 2-0 up in the fourth.
  Ferrer, 33, refused to yield and hit straight back but Murray made the decisive move in game six after the Spaniard netted a smash and made it to the finish line with two hard-fought service games.
  He will now play Raonic, who is pledging to "fight with all my heart" when the two meet on Friday.
  With Jamie Murray through to the semi-finals of the men's doubles with Brazilian Bruno Soares, it is the first time two brothers have reached semis in singles and doubles at the Australian Open.
  Azarenka might have been seeded seven places lower than Kerber at 14th, but the German still pulled off something of a shock by knocking out the Belarusian.
  The 28-year-old raced into an early 4-0 lead and then staged a superb second-set fightback to beat two-time champion Azarenka 6-3 7-5.
  The German had lost all six previous matches against Azarenka and saved five set points from 2-5 in the second set.
  "I can't actually describe it in words," said Kerber. "I'm so happy I beat her for the first time."
  Azarenka, 26, said her footwork and shots weren't good enough and also blamed "too many unforced errors in the key moments".
  BBC Radio 5 Live tennis correspondent Russell Fuller:
  Winning the Davis Cup with Serbia for the first time in 2010 inspired Novak Djokovic to win three Grand Slam titles the following year.
  Andy Murray certainly believes you can also ascribe some of the British success in Melbourne to Davis Cup momentum.
  "When you have success like we had, the other players see that and want to be part of that as well," he told BBC Sport.
  "Jo's played great pretty much since Wimbledon last year and my brother has probably taken some confidence from the Davis Cup as well.
  "They were very intense atmospheres and he played some of his best tennis in those matches."
  Will the run continue when Konta takes to the court for her semi-final?
  "Jo's definitely got a chance," said Murray. "I think she's playing at that level now. I don't think there's a clear favourite."
target: Britain have two Grand Slam singles semi-finalists for the first time since 1977 after victories for Johanna Konta and Andy Murray at the Australian Open.