We've written several times about Mexico's challenge to the imposition of U.S. death sentences to 52 Mexcian nationals in the International Court of Justice in the Hague, see here, here, here and here. Essentially, the dispute is this (from our prior post):

Mexico filed suit against the US in the International Court of Justice in the Hague over the U.S.’s failure to comply with the Vienna Convention’s guarantee of allowing foreign nationals access to consular officials prior to interrogation. Mexico is also seeking provisional measures, essentially a temporary restraining order, against all capital prosecutions in the US against Mexican nationals until the case is resolved.

Adam Liptak of the New York Times brings us up to date:

There is little dispute that the United States violated the treaty in most or all of the 52 cases before the court in The Hague. The core issue during several days of arguments before the court last month was what should follow from that.

In March, the [State] department's top lawyer acknowledged in a speech to state attorneys general that the pending executions were a matter of concern. "We have had a number of conversations with government lawyers in both states about these cases," the lawyer, William Howard Taft IV, said. In November, Mr. Torres asked the United States Supreme Court to honor the international court's interim order staying his execution. The Supreme Court declined to hear the case. Justices John Paul Stevens and Stephen Breyer indicated that they would be inclined to consider it once the international court rendered its final judgment.

"The answer to Lord Ellenborough's famous rhetorical question, `Can the Island of Tobago pass a law to bind the whole world?,' may well be yes," Justice Breyer mused, "where the world has conferred such binding authority through treaty."

While the 52 inmates sit on death row, awaiting a ruling from the 15 judges in the Netherlands, the parties positions are clear: