When the Smithsonian’s National Portrait Gallery was preparing the wall text in 2014 to accompany an image of the boxer Floyd Mayweather Jr., the museum decided to note that Mr. Mayweather had been “charged with domestic violence on several occasions,” receiving “punishments ranging from community service to jail time.”

Such context is common for controversial subjects in art. But far less so for artists themselves — centuries of men like Picasso or Schiele who were known for mistreating women, but whose works hang in prominent museums without any asterisks.

Now, museums around the world are wrestling with the implications of a decision, by the National Gallery of Art in Washington, to indefinitely postpone a Chuck Close exhibition because of allegations of sexual harassment involving potential portrait models that have engulfed the prominent artist in controversy. Mr. Close has called the allegations “lies” and said he is “being crucified.”

The postponement news on Thursday has raised difficult questions about what to do with the paintings and photographs of Mr. Close — held by museums like the Metropolitan Museum of Art in New York, the Tate in London and the Pompidou in Paris, as well as by high-spending private collectors — and whether the work of other artists accused of questionable conduct needs to be revisited or recontextualized.