World number two Serena Williams is not underestimating unheralded but high-flying Mirjana Lucic-Baroni as she looks ahead to a meeting with the fairytale story of the Australian Open.

Williams will do battle with Lucic-Baroni in the semi-finals after the 34-year-old veteran upstaged fifth seed Karolina Pliskova in 6-4 3-6 6-4 on Wednesday.

After personal and financial problems, Lucic-Baroni's renaissance continued as she reached the final four of a grand slam for the first time since 1999.

And 22-time major champion Williams is braced for Thursday's clash as she stands in the way of Lucic-Baroni's remarkable run after seeing off Johanna Konta 6-2 6-3.

"She's playing really well. I think it's so important not to underestimate anyone. This has been coming for her for a long time," Williams told reporters.

"She's been wanting to win grand slams and to do well.

"I think it's so important for me to just stay focused and hopefully play well. Hopefully I'll be able to get a win. I'm here to win. I'm here to do the best that I can. So hopefully I'll be able to do well."

The pair's most recent meeting was in 1998 at Wimbledon.

Williams won in straight sets in the second round, not that the 35-year-old American remembers much.

"It was on Centre Court. That's all I remember. I remember winning. I was so excited because I was so young. She obviously was super young, too. That's all," she added.

"Honestly, we have totally different games now, the both of us. We both have gone through a lot. We both have survived, and here we are, which I think is a really remarkable story."

It will be a battle of the veterans on Rod Laver Arena, while sister Venus - who is 36 years of age - is also in the final four against Coco Vandeweghe.

Asked what it says about tennis with veterans still vying for grand slams, Williams added "I feel like we've been just going. I've been doing this for many years. The past few years I've been super consistent.

"I'm just really happy for Venus, obviously. She's doing amazing. I'm really happy for Mirjana, as well. Like I said, I was there when she first started. To see her be able to never give up actually is super inspiring to me. It's a wonderful story.

"At the end of the day, it really helps me to realise that you have to always go for your dreams. So I feel like it's just great."