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Heidi Klum and Seal, Robert DeNiro and Grace Hightower, Robin Thicke and Paula Patton—just a few of the high-profile couples who have brought interracial relationships into the public eye. Forty-three years ago, these marriages would have been illegal in many US states. But in 1967, the Supreme Court overturned those bans, and by 2007, 77% of Americans said they approved of interracial unions between black and white couples.

So it was shocking when Keith Bardwell, a Louisiana justice of the peace, refused—in 2009—to marry a black man and a white woman. Bardwell contended that mixed race marriages don’t last, and the children they produce “suffer.”

Jarring, yes, but should this incident have come as a surprise? Crossing racial lines in love sparks frequent debate. Singer-songwriter John Mayer recently offended fans (and non-fans) when he told Playboy—complete with racist language—that he isn’t attracted to black women. Disney garnered criticism for pairing its first black princess, Tiana in The Princess and the Frog, with a prince who doesn’t share her racial background. Clearly, this intimate variety of integration still has the potential to cause a stir.

The nation’s first law prohibiting marriage between races was enacted in Virginia in 1661. By 1924, 38 states had similar laws. But that changed when a white man named Richard Loving and his African-American and American Indian fiancée Mildred Jeter were prevented from marrying in Virginia. The couple challenged the state, and on June 12, 1967, the Supreme Court declared it unconstitutional to bar a marriage on account of race.

Although only about 8% of American marriages are interracial, dating between races is more common. In the US, the odds an adult has dated someone of a different racial background are 1 in 2.08. Hollywood’s getting on board, too: Grey’s Anatomy, Gossip Girl, Brothers and Sisters, and Modern Family are among the popular programs that have featured mixed relationships in recent seasons.

The increase in these relationships on and off-screen might suggest that they’re now nothing out of the ordinary. On television, most mixed race couples are spared any discrimination. But in reality, interracial couples still face obstacles in their families and communities. Montgomery County, Georgia has held separate proms for black and white students since 1971, when the district’s schools were first integrated. Until 2000, dating across racial lines was banned altogether at Bob Jones University in South Carolina.

Attempts to curb cross-racial interactions between young people reflect lingering concerns among older generations. Young adults are much more likely to approve of dating interracially than their grandparents. The odds an adult between the ages of 18 and 29 approves of a black/white relationship are 1 in 1.05, or 95%, while the odds are only 1 in 2.22 that an adult 65 or older will approve of a white woman dating a black man (1 in 2.17 seniors think the opposite pairing is appropriate). So while it might be cool for a young white guy to introduce his black girlfriend to his college buddies, taking her home for Thanksgiving could be a whole different story. Announcing a wedding might be more difficult still.

But there’s reason to be cautiously optimistic. The numbers suggest that in the next generation, discomfort with multiracial families should continue to dissipate. As the young people who say they approve of interracial relationships raise children of their own, they will—hopefully—create a stronger climate of acceptance.

In Montgomery County, students say they’d like to have one prom with all their friends. To do so, they’d have to challenge nearly 400 years of racial separation. For their own kids, maybe they’ll make it happen.