The public inquiry into undercover policing may "expose both creditable and discreditable conduct", chairman Lord Justice Pitchford has warned.
The proceedings in London will be "the first time that undercover policing has been exposed to the rigour of public examination," he told a court.
Helen Steel, who had a relationship with an undercover officer, said police committed "human rights abuses".
But police said undercover officers can play an important role.
Lawyers investigating allegations for the Home Office say they have uncovered more than 80 possible miscarriages of justice relating to undercover policing.
Investigations revealed officers had also had relationships with women while undercover, and had used the names of dead children.
Undercover: The allegations made to date
- Some men had relationships with women who did not know their lover was an undercover police officer
- At least 42 of 106 covert identities were the names of children who had died - but there could be more
- Labour MPs, trade unionists and justice campaigns, such as anti-racism groups, were targeted
- An officer was inside the "wider" Stephen Lawrence campaign - and briefed superiors as they campaigned against Scotland Yard failings and prepared their defence ahead of the public inquiry into his murder
- Undercover officers were arrested alongside other campaigners - leading to claims of miscarriages of justice
- Some 57 convictions have been quashed to date - and there could be more than 80 more
Opening proceedings at the Royal Courts of Justice, Lord Justice Pitchford said: "It seems likely that the inquiry will expose both creditable and discreditable conduct, practice and management.
"At the conclusion of its investigation, the inquiry will report to the home secretary and make recommendations as to the deployment of undercover police officers in future."
"Jacqui", who had a son with a man she thought was a fellow animal rights activist, did not discover he was an undercover police officer until 25 years after he disappeared from her life.
She told the BBC the discovery was "like an earthquake".
"I want this inquiry to really get to the truth... and come to some conclusion about whether this money and human misery was worth it".
She wants the officers themselves to have the chance to give evidence, perhaps anonymously, "and not have to worry about the Official Secrets Act or what's going to happen to them".
She hopes "what happened to me... what happened to other women, will never happen again.
"There is no circumstance where having sexual relations in order to get information on a group, whatever the group is, is ever justified."
The home secretary ordered the review after claims police spied on the family of Stephen Lawrence.
Neville Lawrence, Stephen's father, said more than one judge should oversee the case, or its conclusions should be left to a jury.
"You have an old saying - two heads are better than one," he said. "Sometimes one person might miss something and the other one can bring them back to where they're supposed to be".
And Ms Steel said: "These undercover policing units have committed grievous human rights abuses which are absolutely shocking in a supposedly democratic society. We want to make sure they don't happen again to anybody else, and for that to happen we need the full truth to emerge."
"Alison" was a member of an independent political group in London in the 1990s when she formed a relationship with a man she knew as Mark Cassidy. They were together for five years and lived together for four.
But Mark disappeared suddenly, saying he'd had a row with his mother and was depressed.
"His disappearance five years after we met was very sudden and unexpected and didn't make sense. I spent a long time trying to find out where he was and why he'd left," Alison told Radio 4's Today programme.
She believes claims of depression were part of an "exit strategy" used by officers.
"I knew I had to get on with my life and I did that, but still carried on looking and searching when I could," she added.
She later found out "Mark" had a wife and children.
"I've carried on with my life, I've met somebody else who I grew up with as a child which was the only reason I was able to trust them was because I knew that they were who they said they were.
"And I've been fortunate enough to have a family, but many of the women who this has happened to have not been so fortunate."
Lord Justice Pitchford's inquiry at the Royal Courts of Justice will look into police infiltration of political and social justice groups in England and Wales since 1968.
The inquiry is expected to be split into three parts: establishing what happened, examining the procedures adopted by police to prevent wrongdoing, and recommendations for the future.
Preliminary hearings are due to start in the autumn and the inquiry is set to last three years.
The inquiry's terms of reference include:
- Examining the motivation and scope of undercover police operations
- Looking at their impact on individuals
- Establishing how operations were authorised and overseen
- Discovering how much officials and ministers knew
The allegations were first widely reported in 2011 when a former undercover officer, Mark Kennedy, offered to help defend, in court, six environmental campaigners whom he had infiltrated.
That trial collapsed - and later the same year, there were further revelations of undercover relationships, one of which led to a child.
By Dominic Casciani, BBC home affairs correspondent
The allegations of wrongdoing by undercover police officers that have emerged since 2011 have been extraordinary.
That steady stream of stories has led to the launch of a major public inquiry into their activities.
The breadth and nature of what is being alleged is almost too big to grasp, but it fundamentally comes down to a simple question of whether elements of the police were out of control.
Seven key issues the inquiry will examine.
Metropolitan Police Commissioner Sir Bernard Hogan-Howe said undercover policing was an important tactic, but had to be done legally.
He told BBC London: "We, for the police, will make the case that our undercover officers are incredibly brave and they deal with some very dangerous people.
"We think this is a vital part of our toolset and if we don't have it then we don't suffer, but the public might.