Mr Depp, 58, sued his ex-wife for $50m (£40m) for an article she wrote in which she claims to be an abuse victim. Ms Heard, 36, counter-sued for $100m.
Mr Depp's lawyer asked jurors to "hold Ms Heard accountable for her 'lies'".
Ms Heard's team, in turn, said it was Mr Depp who is a bully and abuser, not to be trusted.
The jury of seven must come to an unanimous decision for a verdict. They began their deliberations shortly after both sides delivered their closing arguments.
Benjamin Rottenborn, a lawyer for Ms Heard, reminded jurors of explicit text messages between Mr Depp and his friends, telling them he wanted to visit harm upon his ex-wife.
"This is a window into the heart and mind of America's favourite pirate," Mr Rottenborn said. "This is the real Johnny Depp."
Mr Depp's lawyer Camille Vasquez, in contrast, called Ms Heard's allegations of abuse "wild, over the top and implausible".
"There is an abuser in this courtroom, but it is not Mr Depp," Ms Vasquez said, replaying an audio recording in which the actress admits to hitting her then-husband.