Some of that confusion is owed to the fact that the opinion was written by Justice Harry Blackmun, the only one of America's 112 Supreme Court justices to sped most of his prejudicial legal career defending doctors, as counsel for the Mayo Clinic. Doctors, not women, were the targets of abortion prosecutions.
As Justice Ruth Bader Ginsburg noted last year, Roe "wasn't woman-centered, it was physician-centered." And, as she has noted, abortion law was already rapidly changing when the case was decided in January 1973.
In the five years before Roe, 16 states with 41 percent of the nation's population had liberalized their abortion laws. When the decision was announced, almost every state legislature was beginning its session, and many likely would have passed similar legislation.
The result has been that abortion has become a national political issue. Initially, the abortion issue split both parties. More recently, it has come to define them.
Today there are few pro-life Democratic politicians or pro-choice Republicans. In Europe, in contrast, where abortion has been legalized with varying restrictions, it has seldom been a matter of partisan controversy.
Amid the controversy, public opinion on abortion has remained relatively constant for many years and fully endorses neither the pro-life nor pro-choice positions.
In the unlikely event that Roe v. Wade were overturned, perhaps a few legislatures -- Utah? Louisiana? Guam? -- would prohibit all abortions. But not many. It's hard to criminalize behavior that people have been told is a right, even one as vaguely defined as Justice Blackmun's "privacy."
Witness the resistance to prohibition of gun ownership, albeit opponents on this issue have a constitutional text guaranteeing the "right of the people to keep and bear arms." Gun ownership continues, and so will abortion.
But with this difference: Gun sales have been booming during the Obama presidency, but the number of abortions has been declining for many years. The peak abortion rate per population was reached in 1981, according to the pro-abortion rights Guttmacher Institute, whose data are accepted on all sides.
As population rose, the absolute number of abortions increased to a peak of 1.6 million in 1990. Since then, the number declined to 1.2 million or perhaps below.
Guttmacher analysts blame this on restrictive laws. They note that 35 states require parental notification or consent for minors' abortions and that Congress forbids Medicaid funding of abortions.
They point out that court decisions forced 17 states to fund abortions for low-income women and four more states do so voluntarily, and that 20 percent of women receiving abortions report they got Medicaid funding. Allow it in other states, they imply, and more women would choose abortion.
Further restrictions imposed by states since 2010 -- requiring counseling, banning abortions after 20 weeks, cutting Planned Parenthood funding -- may further reduce the number of abortions.
But these restrictions are in line with public opinion that, as my American Enterprise Institute colleague Karlyn Bowman has documented, has remained steady over many years.
Most Americans think abortion is wrong and should be illegal in some circumstances. Somewhat more believe it to be morally wrong than morally acceptable.
Very large majorities would allow it for physical health reasons and in cases of rape. But very large majorities also favor 24-hour waiting periods, mandatory counseling, parental consent and husband notification.
Very large majorities also oppose second- and third-trimester abortion and support the 2003 federal law banning partial-birth abortion.
These opinions are rooted in the recognition by most Americans that abortion ends a human life.
Abortion advocates have long argued that a woman should have control over her body. But these people, many of whom argue that conservatives ignore science on other issues, ignore science on this one.
Science tells us that the fetus and the mother have different DNA, that they are separate people and not part of the mother's body, over which advocates insist she have control. A fetus is not the equivalent of a mother's fingernail.
Sonograms, unavailable in 1973, reinforce that impression. Their availability may be making abortion less attractive to young women.
The murder conviction of Philadelphia abortionist Kermit Gosnell showed that restrictions on abortion clinics are needed and are not just "a war on women."
Justice Blackmun thought he settled the abortion issue forever. Forty-one years later, the debate goes on.