Depp's lawyers filed the U.S. case in Fairfax County, Virginia, because the Washington Post is printed there. The newspaper is not a defendant.
Both sides have claimed damage to their Hollywood careers.
Heard's legal team presented an entertainment industry expert who estimated that the actress has suffered $45-50 million in lost film and TV roles and endorsements.
An industry expert hired by Depp's side said the actor has lost millions because of the abuse accusations, including a $22.5 million payday for a sixth installment of "Pirates".