|Venue: Flushing Meadows, New York Dates: 29 August-11 September|
|Coverage: Live radio commentary on Radio 5 live sports extra from 22:00 BST plus live text coverage on selected matches on the BBC Sport website.|
Fourth seed Agnieszka Radwanska saved four set points on her way to beating British number three Naomi Broady in the second round of the US Open.
The Pole came back from a break down and edged a dramatic tie-break before going on to win 7-6 (11-9) 6-3.
"I need to play aggressive tennis," Broady said. "I need to keep working on my serve. It was better at the start of the year."
Top seed Serena Williams beat fellow American Vania King 6-3 6-3.
Broady, ranked 82nd, was playing in the second round of a Grand Slam, and up against a top-five opponent, for only the second time in her career.
Williams, chasing record seventh US Open and 23rd Grand Slam singles titles, earned her 306th Grand Slam win to tie Martina Navratilova's all-time record.
Romania's Simona Halep, the fifth seed, beat Czech Lucie Safarova 6-3 6-4, while sixth seed and two-time former champion Venus Williams beat Germany's Julia Goerges 6-2 6-3.
She was serving unbelievable - Radwanska
Radwanska could overtake Serena Williams and become world number one if results go her way at Flushing Meadows - but she was given a severe test by Broady on Louis Armstrong Stadium.
The 26-year-old from Stockport used her 6ft 2in frame to regularly send down serves above the 120mph mark, backing them up with 35 winners from the net and some flashing groundstrokes.
"She was serving unbelievable," Radwanska said. "120mph serves are not easy to return."
Radwanska, 27, recovered from 5-2 down to earn a tie-break in the first set and saw off four set points, with Broady failing to make three returns and sending a volley long.
It was Radwanska who prevailed when a Broady forehand floated long, but it had taken the former Wimbledon finalist 69 minutes to take the set, and she found herself 2-0 down in the second.
The errors were increasingly coming from Broady's end of the court, however, and Radwanska levelled at 2-2 before firing a backhand winner from out wide to get the decisive break at 4-4.
"I'm so pleased I could come back in that first set," said the Pole. "It was the key set. There was a lot of running and a lot of struggling but it was another two sets for me."