Mallorca Open 2017 champion Anastasija Sevastova cruised into the last eight, while fourth seed Elise Mertens beat Samantha Stosur.
Top seed Naomi Osaka edged past Greece's Maria Sakkari 6-1 4-6 6-3 in round one of the Birmingham Classic.
Former Wimbledon champions Angelique Kerber and Maria Sharapova will do battle at the Mallorca Open this week.
Sofia Kenin overcame Kirsten Flipkens at the Mallorca Open, where Elise Mertens also progressed courtesy of a win over Andrea Petkovic.
Karolina Pliskova and Johanna Konta were victorious at the Birmingham Classic, but Elina Svitolina suffered a first-round exit.
A tough Nottingham Open final saw Caroline Garcia come out on top, edging past Donna Vekic on Sunday.
American Alison Riske fought back from a perilous position to beat top-five star Kiki Bertens and land her second WTA Tour title.
World number four Kiki Bertens was forced to retire from the French Open due to illness, but could add to her list of honours this weekend.
Caroline Garcia swapped a grass court for a hard court to win in Nottingham, while Kiki Bertens was frustrated by rain in her homeland.
Kristina Mladenovic and Donna Vekic were among the winners in the first round of the Nottingham Open.