Conservatives arriving at their conference in Manchester faced "up to 30,000" people taking part in various protests, according to police.
Anti-austerity protesters calling for the Tories to be kicked out of power took part in a large march and rally. There was also an anti-Brexit march.
Three protesters were arrested after wheelchair-users blocked tram lines in St Peter's Square.
Greater Manchester Police said there were no other arrests.
Thousands of Labour supporters, union members and members of other left-wing parties waved placards, wore fancy dress and chanted "Oh, Jeremy Corbyn" as they took part in the The People's Assembly march against austerity.
As police helicopters hovered overhead, a trade union leader called for a general strike on public sector pay to "bring the Tories down" in a speech in Piccadilly Gardens.
PCS leader Mark Serwotka claimed Conservative policies were "literally killing people," referring to cuts to health and safety rules and the Grenfell Tower fire tragedy.
The Communist Party said it was giving Theresa May "notice to pack her bags and quit" and claimed "mass action will drive the government out".
Rail, Maritime and Transport Workers union boss Mick Cash said the "only way do that is through a general election".
Demonstrators, some wearing masks to hide their identity, were involved in a stand-off with police close to the conference venue, in St Peter's Square, for nearly two hours.
Dozens of officers surrounded the protesters, as a group of wheelchair users blocked two tram lines.
Two women were arrested on suspicion of obstructing a highway. A man - who is not thought to have been a wheelchair-user - was arrested on suspicion of assaulting an officer.
Meanwhile, anti-Brexit protesters heard speeches from Conservative former health secretary Stephen Dorrell and Lib Dem leader Sir Vince Cable, who demanded a vote on the final Brexit deal.
European Movement chairman Mr Dorrell told the rally that people should be given the "opportunity to change their minds".
Quoting his former boss Sir John Major, Mr Dorrell said Brexit would be a "historic mistake".
He said: "Many people say to me I'm flying in the face of democracy. What is undemocratic about changing your mind?"
Sir Vince said there was a "civil war" going on at the Tory conference between the prime minister and Foreign Secretary Boris Johnson.
Broadcaster Terry Christian hit out at "spineless" Greater Manchester mayor Andy Burnham for refusing to oppose the Brexit process.
Chief Superintendent John O'Hare, who is leading the conference policing operation, said: "Up to 30,000 people came in to Manchester city centre today (Sunday 1 October 2017) to take part in various protests."
He added: "The vast majority of people exercised their democratic right to protest and did so in the spirit of their causes.
"No arrests were made during the marches and this is a testament to those who attended and the organisers who took responsibility for the events and worked closely with us to ensure a safe and successful operation."