Jair Bolsonaro has spoken in support of torture and said he would rather his son die than be homosexual.
The former army captain's rise to power has been marked by divisive rhetoric and derogatory remarks about women, gay people and the country's black population.
Dubbed "Trump of the Tropics", Mr Bolsonaro's policies include loosening gun ownership laws and allowing police to use more force.
In April 2017, Mr Bolsonaro described having a daughter as a "weakness". He has also said he would not treat or pay women the same as men.
He said: "I have five children. Four were boys, on the fifth I got weak and had a daughter."
In 2014, he told federal deputy Maria do Rosario at the chamber of deputies: "I would not rape you because you are not worthy of it."
In 2011, he said he would "rather his son die in a car accident than be gay".
In 2002, Mr Bolsonaro said: "I'm not going to combat or discriminate, but if I see two men kissing on the street, I'm going to hit them."
During a speech in Rio in 2017, he said: "I went to a quilombola [settlement founded by people of African origin] in El Dourado Paulista.
"Look, the lightest African descendant there weighed 100 kg. They don't do anything. They don't even serve to reproduce."
Mr Bolsonaro said he was "in favour" of torture while referring to then-president Fernando Henrique Cardoso in 1999.
Reiterating his stance on torture in 2000, he said: "I defend torture. A drug dealer who acts on the streets against our children must to be immediately put on a pau-de-arara [torture device where the person is tied up on a pole that resembles a bird's perch).
"There would be no human rights in this case. There would be pau-de-arara, beating. The same thing for kidnappers. The guy must be broken to open his mouth."
During a campaign event in September 2018, he said: "Let's shoot all the PT members here in Acre [a Brazilian state]."
In 2000, he said: "I never beat my ex-wife. But I thought of shooting her various times."
After criticising Brazil's government during an interview in 1999, Mr Bolsonaro was asked if he would shut down congress if he was elected president.
He said: "There is no doubt. I would perform a coup on the same day. [Congress] doesn't work.
"And I am sure that at least 90% of the population would celebrate and applaud because it doesn't work. The congress today is useless… let's do the coup already. Let's go straight to the dictatorship."
Mr Bolsonaro provoked considerable controversy over remarks made about birth control in 2008, when he appeared to advocate the sterilisation of poor people.
He said: "We need to adopt a rigid birth control policy... People who aren't prepared to have children, shouldn't have them...
"Methods [of birth control] have to be provided for those who, unfortunately, are ignorant and have no means to control their offspring because we [as upper middle class] are able to control ours. Poor people don't control [theirs]."