Here's a summary starting with those who want to keep marriage laws as is, a group that includes the state's traditional power brokers:
The State of Utah • The attorneys general of 17 states, including Utah, say current marriage laws may impact gay Americans, but they were not drafted to target them, and therefore, the court should not consider them a protected class.
"The traditional definition of marriage has always been about the need to encourage potentially procreative couples to stay together for the sake of the children their sexual unions may produce, not about animus towards homosexuals," they argued.
The AGs also argue that finding gay-marriage bans unconstitutional would "cause irredeemable harm to the nation as a deliberate, democratic society," on par with the political tumult surrounding abortion rights.
Republican senators • Sen. Orrin Hatch, R-Utah, led the Judiciary Committee in 1996 when Congress overwhelmingly passed DOMA and he continues to support it today.
He led a group of nine colleagues who filed a brief focused on federal reasons for defining marriage as between opposite-sex adults, noting the law only restated existing practice, since before DOMA gay marriage was not legally recognized.
They said DOMA maintained "certainty in the application of federal law," avoiding legal challenges on legal benefits given to married couples. And they said by offering federal benefits to only straight couples, the government protected each state's ability to "preserve traditional marriage."
Their brief states: "If federal benefits were available for same-sex couples validly married under state law, however, federal law would serve as an incentive for state recognition of same-sex marriage."
The LDS Church • Utah's dominant faith joined five religious groups in defending DOMA in a brief that was written by The Church of Jesus Christ of Latter-day Saints' Utah-based law firm Kirton McConkie.
The faiths argue that the gay-marriage issue shouldn't be seen as a fight for equal rights for "a discrete and insular minority" but as a cultural debate over the very meaning of marriage, and they don't believe the court should settle the matter.
They depict a policy fight among those who see marriage as "inherently oriented toward procreation and child-rearing" and those who view marriage "as primarily a vehicle for affirming and supporting intimate adult relationship choices," and they think it is one that should continue to play out in state legislatures and Congress.
"We have just as much right as anyone else to have our views considered by democratic decision makers," the brief states. "But that cannot properly occur if the great marriage debate is removed from our democratic institutions."
Social science professors • Two Brigham Young University professors joined five of their colleagues to challenge a claim by the American Psychological Association that there's no difference in the outcomes of children raised in straight or gay households.
The educators, including BYU's Alan Hawkins and Joseph Price, argue the APA is relying on non-random studies of limited scope.
"What is clear is that much more study must be done on these questions," their brief states, "But there is no dispute that a biological mother and father, provide, on average, an effective and proven environment for raising children."
Not to be outdone, a number of Utahns who support broader recognition of gay marriage also weighed in, including a former governor and the state's large gay community. Here's a summary of their arguments:
Utah Pride Center • Twenty-seven gay rights groups signed onto a brief led by the Utah Pride Center and loaded with references to Utah's ban on gay marriage and cases of discrimination in the state.
It seeks to tie efforts to legalize gay marriage to the fights for civil rights and equal rights for women, just as President Barack Obama did in his second inaugural address by referencing landmark locations in those movements.
"The promise of America will not be realized until there is legal equality for gay Americans everywhere not just at Stonewall and in Seneca Falls, but also in Selma, Sacramento and Salt Lake City," the filing states.
They argue that not recognizing legal gay marriages perpetuates discrimination and bullying against members of the lesbian, gay, bisexual and transgender community throughout the country.
Gov. Jon Huntsman • A large group of prominent Republicans, including former Utah Gov. Jon Huntsman, signed onto a brief asking the court to strike down California's gay-marriage ban. Huntsman, like most of the signatories, previously opposed gay marriage, but said the examples of gay unions in states like Massachusetts show "that there is no legitimate, fact-based reason for denying same-sex couples the same recognition in law that is available to opposite-sex couples."
These Republicans argue that allowing gay couples to get a civil marriage and the benefits that accompany that "poses no credible threat to religious freedom or to the institution of religious marriage."
Campaign finance experts • A bipartisan group of former federal election commissioners signed a brief arguing that DOMA inhibits married gay and lesbian couples from donating to campaigns in the same way that straight couples can, undercutting an individual's right to political expression.
The brief was drafted in part by University of Utah alumni Bryson Morgan and Matt Sanderson, members of the Caplin & Drysdale law firm.
The brief argues that gay spouses are now barred from attending fundraisers hosted by corporations and unions, which are restricted to executives and their spouses. Gay candidates for office also can't spend as much as they want from bank accounts jointly controlled with their spouse, though straight candidates can.
Sanderson, a Mormon, called DOMA an "unconstitutional blunderbuss," and he doesn't think that opinion creates any tension with his faith.
"There is room in the church that I know and love for disagreement on public policy matters," he said. "And everyone I know in the church would, I think, agree with the brief's core premise that an American's right to free speech and association should never hinge on sexual orientation."
Law professors • The University of Utah's Laura Kessler joined 41 other law professors in arguing that having children is not a core purpose of marriage, a major argument made by Republican lawmakers. The professors say there's no legal basis for the law to favor biological children over those who are adopted or conceived through surrogates.
"Federal law and policy reflect a deep commitment to the welfare of all children, whether or not they are raised by their biological parents," they wrote.
The professors do contend that marriages can create stable households for raising children and they see the current legal restraints on the federal level as blocking gay families from those benefits.
The brief states: "DOMA's sole effect is to harm married same-sex couples and their children, while leaving opposite-sex couples [and their children] untouched."