Alvarez, you'll recall, was convicted under the federal Stolen Valor Act for lying about having been awarded the Medal of Honor. In August, 2010, that conviction was overturned by the U.S. Ninth Circuit Court of Appeals on the grounds that the conviction violated Alvarez's First Amendment rights.
Then, this past March, the full Ninth Circuit Court passed on rehearing the case. The prosecution appealed to the Supreme Court, which will now determine whether the sort of lying Alvarez did was a criminal act or a protected form of speech.
The New York Times has an article summarizing the case to date:
The full Ninth Circuit declined to rehear the case. Chief Judge Alex Kozinski concurred, saying that a ruling against Mr. Alvarez would be “terrifying,” as it would allow “the truth police” to censor “the white lies, exaggerations and deceptions that are an integral part of human intercourse.”
In a dissent, Judge Ronald M. Gould said the “lack of any societal utility in tolerating false statements of military valor” justified the law. He rejected the slippery slope argument, saying that “making false statements about receiving military honors is a carefully defined subset of false factual statement not meriting constitutional protection.”
In urging the justices to hear the case, United States v. Alvarez, No. 11-210, Solicitor General Donald B. Verrilli Jr. argued that Congress was entitled “to guard against dilution of the reputation and meaning of the medals.”
Whatever the outcome of the federal case, Alvarez was also convicted in 2009 in LA County Superior Court in a felony insurance fraud case for lying about being still married to an ex-wife. Alvarez lied about that to get the woman covered under his Three Valleys health insurance plan after he was elected. He was removed from office after the conviction.