More embryos than are needed are often created and, as correspondent Lesley Stahl reports, it's these surplus embryos that are at the center of a huge controversy because they contain very special stem cells that scientists believe are extraordinary, and have great promise of one day curing a range of diseases.
Caught in the middle of the controversy are couples like Kai Madsen and his wife Pam, who runs an advocacy group for infertile couples.
"Our personal story has become this lightening rod issue for this country," says Pam. "These embryos, they're our personal story."
The Madsen's personal story began with their having a heck of time getting pregnant.
"It was not totally her. It was not totally me. It was a combination factor, and we started with the IVF programs," explains Kai.
Asked what the programs do, Pam explains: "They want to make many eggs. They want … many embryos."
"The best chances … of creating healthy embryos for implantation later," her husband adds.
With the medication regimen she was on, Pam made 27 eggs. "I was a regular chicken," she jokes.
Like most couples who go through fertility treatments, the Madsens ended up with excess embryos. They have four that have been frozen ever since the birth of their second son, 13 years ago.
Did they think they would have to decide about what to do with those excess embryos?
"No. When you go through this process, your expectations are not really very high," says Kai.
Pam adds that most people going through the process are skeptical they will have a baby and that a surplus of embryos is not something you think about at the time.
There are thousands upon thousands of couples like the Madsens. In fact, there are 400,000 frozen embryos in storage in fertility clinics across the country.
Dr. Richard Scott, who runs a fertility clinic in Morristown, N.J., stores 7,000 frozen embryos in large liquid nitrogen tanks.
"In each, there will be one cane for each patient that will hold all of the embryos that they have frozen," Scott explains.
It can cost a couple up to $2,000 a year to store their excess embryos, which are frozen at 321 degrees below zero. It's been suggested that fertility clinics should stop making so many embryos that go unused.
"You're really limiting, then, the number of eggs that you can inseminate," Scott says. "Then you're actively intervening to harm that couple and reduce their chances of ever having a baby. I have a very big ethical problem with that."
Scott cultures as many as 12 embryos per couple, implants two to four and freezes the rest for use, should the first attempt fail. That, he says, cuts down on the expense and emotional toll.
Many of the couples are now in the position the Madsens are in: of deciding the fate of their surplus embryos.
The Madsens say there are five options.
"Well, one, we could have used them to have a third child, the potential of a third child. We could have destroyed them, not used them and … have them thawed and put away. We could have donated them to another couple who's having reproductive difficulties and wants to have a baby. We could continue to do nothing. Or we could donate them to medical research," Pam explains.