The answer: help rich people pay less in taxes.

In the case of Mr. Black, the chief executive of Apollo Global Management, his advice could have been worth as much as $2 billion in savings, according to a law firm’s review of Mr. Black’s business dealings with Mr. Epstein. On Monday, Mr. Black announced that he would step down as Apollo’s chief executive this year after the review found he had paid Mr. Epstein $158 million over five years for his services.

Mr. Epstein’s specialty was suggesting ways for wealthy clients to use sophisticated trusts and other investment vehicles to reduce their tax liability while passing on assets to their children, according to documents reviewed by The New York Times and interviews with 11 people familiar with his work. In the process, he collected hefty fees — usually based on a cut of the anticipated tax savings.