A little more than forty years ago, one of the first attempts at in-vitro fertilization ended when the chairman of the OB-GYN department at New York's Columbia-Presbyterian hospital took the test tube containing the growing embryos out of the incubator that was keeping them alive. The doctor who'd been growing them hadn't asked permission, and the chairman had plenty of reasons to step in—the equipment wasn't sterile, the hospital could be liable if the baby turned out wrong, the experiment was against federal regulations.

But within just a few years the first IVF baby was born, in England. She was a healthy baby:

She's now 36, with babies of her own. The first IVF baby in the U.S. followed a few years later, in 1981, and now about one percent of all babies born in the U.S.—more than 65,000 babies each year—are conceived using some form of assisted reproductive technology.

In the past 10 years or so, the use of these techniques has doubled, the Centers for Disease Control and Prevention says; it's become so popular that there's now an abundance of unused embryos in America's medical freezers. Part of the reason the use of IVF has grown so quickly in popularity is that a surprisingly large number of people—about one in eight, in the U.S—have some fertility issues.

As IVF has become routine, doctors have added to its powers, too. Four decades ago, no one had ever conceived a baby from an embryo created outside a woman's body. Now, doctors can sequence every letter of the genomes of IVF embryos and screen for genetic abnormalities. They can avoid diseases connected to mitochondrial DNA by creating embryos from three donors—one for the egg, one for the sperm, and a third for the mitochondria—all of whom transfer heritable DNA to any baby that results. Just last year, a team in Japan succeeded in reviving ovaries of women who had, essentially, entered menopause years earlier than most.

Some researchers are trying to make this relatively expensive sequence of treatments more affordable too. There are now ovary-stimulating drugs that can be taken orally, instead of via more expensive injections. And one low-cost design, for instance, is about the size of a shoe box—instead of a fancy incubator the embryos grow inside an aluminum heating box (although, as the inventors of this system told to BBC, a thermos worked, too). Turns out, embryos aren't so picky about where they'll grow—and although there's still plenty of risk that these procedures won't lead to pregnancy, the old-fashioned way is not perfect either.