Quite a bit, it turns out, but romance isn't a part of it, according to the actress's rep.
"Scarlett and Sean are not dating – they have been friends for years. Nothing more, nothing less," her rep says. "They have been talking over the last few months regarding Haiti Relief and Scarlett's upcoming trip to Haiti as Oxfam's Global Ambassador."
Reports had swirled recently that Johansson, 26, had hooked up with Penn, 50, last month following her split from husband Ryan Reynolds, 34.
Reporting by ALEXIS CHIU