Taking the witness stand on week four of the trial, Ms Heard alleged that a pattern of violence began in 2012.
Mr Depp is suing Ms Heard over a story she wrote in which she described herself as a domestic abuse victim.
In his testimony, Mr Depp denied any wrongdoing.
Over several hours of court testimony in Virginia on Wednesday, Ms Heard, 36, recalled her first interactions with the "charismatic" Mr Depp on the set of 2011 movie The Rum Diary in Puerto Rico.
The pair reconnected on a press tour for the film several years later, during which Ms Heard said they "fell in love".
The happiness of the early stages of their relationship, Ms Heard added, were soon marred by disparaging comments he began making in 2012 - the same year she alleges that Mr Depp, 58, struck her for the first time.
In emotional testimony, Ms Heard said it happened when she laughed at a tattoo on his arm that said "Wino" - an alteration to a tattoo he had made during a previous relationship with actress Winona Ryder.
"I laughed because I thought he was joking," she recalled. "And he slapped me across the face."
"I will never forget it," she said.
Mr Depp has denied the incident took place and said in his own testimony that the claim "never made any sense" to him.
In her testimony on Wednesday, Ms Heard sought to portray Mr Depp as someone who could be warm and kind, but who would fly into rages - sometimes at perceived infidelity - when under the influence of alcohol or drugs. She said he tried to conceal his substance abuse, which ranged from drinking spirits to taking "a lot" of cocaine.
"It would be accusations, accusations and then he would explode," Ms Heard said, adding that Mr Depp would slap and "backhand" her. After the fights, Ms Heard said he would "disappear".
"He'd come back clean and sober and he'd be extra nice and extra apologetic and we'd be good again," she added.
Ms Heard also alleged Mr Depp conducted a "cavity search" on her after an altercation during a drug-fuelled desert party in Hicksville, California.
"I just stood there," she said tearfully.
In his own testimony, Mr Depp said he never struck Ms Heard and characterised her as having "a need" for conflict and violence.
The trial is expected to continue for at least another month.
