Good evening and welcome to our LIVE coverage of the US Open women's singles final - Serena Williams v Naomi Osaka.

So we have one singles final decided - a first Grand Slam title for Japan's Naomi Osaka. It's been a fascinating tournament - thanks for your company!

That was an emotional trophy ceremony, with Osaka finding it difficult to speak, and Serena - to her credit - telling the crowd to calm down and stop booing and congratulate the winner.

Osaka has gone to her team and her mum has dissolved in tears. The two are just holding each other and sobbing.

Umpire Carlos Ramos has been escorted off court - he won't be there for the post-match presentation.

Osaka is weeping, possibly with stress as well as sheer happiness.

There's a nice hug between Osaka and Serena at the net - the 36-year-old holds out her arms to the younger woman. Osaka shakes hands with the umpire, Serena has a go at him again.

WILLIAMS 2-6 4-6 OSAKA: Serena has to gather herself as Osaka prepares to serve for the championship - she's been at her seat weeping into a towel. But Osaka is composed, and that serve has been absolutely on the nail all night - she serves an ace to set up double championship point. A forehand down the line from Serena saves one of them - and then an ace gives Osaka her first ever Grand Slam title.

She's still crying.

Serena walks off court to talk to the supervisor again.

WILLIAMS 2-6 4-5 OSAKA: People are booing even when Serena gets a let call. This is absolutely ridiculous. Venus is on her feet cheering her little sister on.

It's Serena to serve, then. The crowd are up in arms.

Serena is now 5-3 down in the second, and she's called for the referee. She's in tears. "This is not fair." The crowd are booing some more.

Serena has been complaining that the coaching violation casts aspersions on her character - but refuses to accept that the verbals she's been dishing out does the same to umpire Ramos.

"You stole a point from me. You're a thief too." And then she gets another violation - and a game penalty.

Serena is still shouting at umpire Ramos. "You owe me an apology. Say it. Say you're sorry."

WILLIAMS 2-6 3-4 OSAKA: That's the break for Osaka! She sends a fizzing passing shot past Williams to take the game.

WILLIAMS 2-6 3-3 OSAKA: Osaka serves out to love and is looking unbothered at the moment.

The crowd are booing, Serena shushes them, and Osaka has to pull things together to serve.