Transgender athletes are having a moment. At all levels of sport, they’re stepping onto the podium and into the headlines. New Zealand weightlifter Laurel Hubbard won two gold medals at the Pacific Games, and college senior CeCé Telfer became the NCAA Division II national champion in the 400-meter run. Another senior, June Eastwood, has been instrumental to her cross-country team’s success. At the high school level, Terry Miller won the girls’ 200-meter dash at Connecticut’s state open championship track meet.

These recent performances are inherently praiseworthy—shining examples of what humans can accomplish with training and effort. But as more transgender athletes rise to the top of their fields, some vocal opponents are also expressing outrage at what they see as transgender athletes ruining sports for cisgendered girls and women.

These issues have come to a head in Connecticut, where a conservative Christian group called Alliance Defending Freedom has filed a legal complaint on behalf of three high school athletes who are seeking to bar transgender girls from competing in the girls category. In Connecticut, as in more than a dozen other states, high school athletes are allowed to compete in the category that matches their gender identity. According to ADF legal counsel Christiana Holcomb, two transgender athletes—Miller and another runner, Andraya Yearwood—“have amassed 15 different state championship titles that were once held by nine different girls across the state.” The US Department of Education’s office for civil rights is now investigating the group’s complaint.

Nowhere are the debates around transgender rights as stark as they are in sports, where the temptation to draw a hard biological line has run up against the limits of what science can offer. The outcome, at least so far, is an inconsistent mix of rules that leaves almost nothing resolved.

In the NCAA, for example, transgender women can compete on women’s teams after they’ve completed one year of testosterone suppression treatment. But the organization doesn’t place limits on what a transgender athlete’s testosterone levels can be. The International Olympic Committee has more granular rules: Transgender women can compete in the women’s category as long as their blood testosterone levels have been maintained below 10 nano moles per liter for a minimum of 12 months. Cisgender men typically have testosterone levels of 7.7 to 29.4 nano moles per liter, while premenopausal cis women are generally 1.7 nmol/L or less. Meanwhile, the governing body of track and field just adopted a 5nmol/L limit.

So which approach is most fair? “Fair is a very subjective word,” says Joanna Harper, a transgender woman, distance runner, and researcher who served on the IOC committee that developed that organization’s current rules. It boils down to whom you’re trying to be fair to, Harper says. “To billions of typical women who cannot compete with men at high levels of sport?” Or “a very repressed minority in transgender people who only want to enjoy the same things that everybody else does, including participation in sports?”

Transgender women’s performances generally decline as their testosterone does. But not every male advantage dissipates when testosterone drops. Some advantages, such as their bigger bone structure, greater lung capacity, and larger heart size remain, says Alison Heather, a physiologist at the University of Otago in New Zealand. Testosterone also promotes muscle memory—an ability to regain muscle mass after a period of detraining—by increasing the number of nuclei in muscles, and these added nuclei don’t go away. So transgender women have a heightened ability to build strength even after they transition, Heather says.