New York City is no stranger to high-profile criminal trials, but few defendants have presented the challenges posed by Mexican drug lord Joaquín “El Chapo” Guzmán, one of the most infamous criminals in modern history.

Opening statements in Mr. Guzmán’s trial will begin Tuesday at the federal courthouse in Brooklyn, N.Y., an undertaking that will require a virtually unprecedented law-enforcement effort to ensure the safety of government witnesses, jurors, other New Yorkers and Mr. Guzmán himself.

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