One of the people said the investigators had seized Mr. Giuliani’s electronic devices. Executing a search warrant is an extraordinary move for prosecutors to take against a lawyer, let alone a lawyer for a former president, and it marks a major turning point in the long-running investigation into Mr. Giuliani. The federal authorities have been largely focused on whether Mr. Giuliani illegally lobbied the Trump administration in 2019 on behalf of Ukrainian officials and oligarchs, who at the same time were helping Mr. Giuliani search for dirt on Mr. Trump’s political rivals, including President Biden, who was then a leading candidate for the Democratic presidential nomination... While the warrant is not an explicit accusation of wrongdoing against Mr. Giuliani, it shows that the investigation has entered an aggressive new phase. To obtain a search warrant, investigators need to persuade a judge they have sufficient reason to believe that a crime was committed and that the search would turn up evidence of the crime.