The allegations released by the National Confidential Forum include child sex abuse, violence and bullying.
Many of the 59 testimonies describe a "veil of secrecy" within institutions, with victims and witnesses scared to speak out.
The majority of those who described their childhood experiences are now aged in their 50s.
However, some were in care as recently as five years ago, while others were sharing experiences from 80 years ago.
The National Confidential Forum, which was set up by the Scottish government in 2014, said it has passed on 38 allegations of abuse to the police.
The forum said most of the abused children came from troubled backgrounds, with many describing being taken into care after physical and sexual abuse within their own family, often accompanied by parental alcoholism, rejection, or neglect.
Once they were in care, the victims described the "distress, fear and confusion" they felt, with many not knowing how long they would be staying in an institution, why they were there, or whether or not parents wanted to maintain contact.
While not all of the 78 people spoken to by the forum suffered abuse, several described how physical, sexual and emotional abuse happened on a regular basis.
For some, abuse was part of a regime of punishment and control that was at the core of the institution in which they lived.
The forum said it had heard about individual abusers carrying out systematic and hidden abuse, as well as accounts of whole staff teams abusing or colluding with the abuse.
One victim described the institution he was sent to as being like a "systematic torture chamber", with "systematic abuse a way of life all the time, morning and night".
Another said: "She'd fill a bath with cold water and throw you in it, with the towel wrapped around your head, which I think is called waterboarding. And then pour buckets of water over your head."
And a third recalled: "They took me into the night duty room and wanted me to do things. They gave me cigarettes to keep it quiet."
Among the allegations contained in its report were accounts of routine forms of punishment such as beating, force-feeding or withholding food or sleep - sometimes apparently being delivered for the enjoyment of the abuser.
Bedwetting was also dealt with severely, with children being forced to sit in a cold bath as punishment, beaten by staff with wet towels, having their head wrapped in a towel and held under running water, and in some cases having to parade around naked with their soiled sheets.
Sexual abuse was talked about by several people and often linked to specific members of staff within institutions.
A veil of secrecy was described in which other children were similarly victimised, witnessed or knew what was happening, but did not speak up.
The forum's report said: "We heard that sometimes the only available love and affection were for the purposes of grooming children for sexual abuse.
"In abusive institutions, people described accepting affection from an adult making them vulnerable to being sexually abused.
"Those who rejected affection for fear of the consequences described missing out on any chance of love and nurturing."
Sense of shame
It also said the child victims were often either too scared to speak out, or the abuse regime represented normality for them, with the children not knowing that adults should not be allowed to behave in abusive ways.
When children did report the abuse, they generally did not remember any action being taken - although at least one person recalled the abuser being removed.
Other responses included the abused child being punished or moved to another institution, which added to the child's self-blame and sense of shame.
Many people also said that adults' views and accounts were always believed over children's, and that this reflected a perception of children in care as "deviant".
After the children left care, generally between the age of 14 and 16, they were often completely unprepared for adult life, lacking in social skills and with nobody to turn to for help and support.
Homelessness continued to be a risk for many well into adulthood, leading to loss of precious belongings, substance misuse and unemployment.
Years of exposure to violence and hardship also increased the risk of getting involved in crime - with some people giving their testimony to the forum from prison.
The National Confidential Forum was set up to allow people who spent time in institutional care as children to come forward and share their experiences, whatever they were.
All hearings, where people tell of their experiences, are "confidential and non-judgmental and aim to contribute positively toward the health and well-being of those who take part".
Separately, the Scottish government has set up an independent inquiry into the abuse of children in care.