LARS LOEKKE RASMUSSEN
Loekke Rasmussen has been in power since 2015. He presently heads a minority center-right government with his Liberal Party, the center-right Liberal Alliance and the Conservative Party.
A member of parliament since 1994, the avid cyclist and jogger also was prime minister from 2009-2011, and earlier was interior and health, and finance minister.
Described as a skilled negotiator, Loekke Rasmussen, 55, has been at the heart of several scandals about using party funds for personal use.
His government has tightened Denmark's immigration laws several times, bowing to pressure from the populist, anti-immigration Danish People's Party, which isn't part of the government but supports it with the needed seats to muster a majority.
Frederiksen, 41, took over Denmark's largest party, the Social Democrats, in 2015 after Helle Thorning-Schmidt lost to Loekke Rasmussen.
A member of Denmark's Folketing, or parliament, since 2001, she comes from a working-class background. Frederiksen was minister for employment and justice in the Social Democratic-led governments of Thorning-Schmidt.
Frederiksen has insisted on forming a one-party government if her party can garner a majority. She started the election campaign with a 16-percentage point lead ahead of Loekke Rasmussen.
KRISTIAN THULESEN DAHL
He became Danish People's Party leader in 2012 after its founder and leader Pia Kjaersgaard voluntarily stepped down.
A member of parliament since 1994, the 49-year-old Thulesen Dahl has in recent years changed his image to become folksier. He has managed to position his party and its 37 seats in parliament by supporting the center-right government in exchange for tightening Denmark's immigration laws.
Thulesen Dahl has said his party shouldn't be in government because it has greater influence by being outside. Polls also have shown people who traditionally voted for the Danish People's Party are drifting to other parties, mainly to the Social Democrats.
Vermund, a 43-year-old architect, founded in 2015 the conservative New Right, which has an anti-immigration and euroskeptic agenda.
The party has been promising a stricter immigration policy in a challenge to the Danish People's Party.
The New Right wants asylum only given to those with "a job in hand," an end to spontaneous asylum, calls for random border controls and wants to limit Danish citizenship to people who "contribute positively" to society.
Vermund has said her party is "ready to withdraw Denmark from the EU and seek a looser connection if a satisfactory agreement for Denmark cannot be achieved."
The 37-year-old lawyer came first to public attention when burning Islam's holy book, the Quran. He did it across the country, often in neighborhoods with a large immigrant population under heavy police protection. Paludan said it was done to support free speech.
The burning of the Quran sometimes sparked violent clashes with counterdemonstrators. Police eventually issued bans, citing Paludan's own safety.
In a video posted on Dec. 19 on the YouTube channel of his party which he founded in 2017, Paludan said: "The enemy is Islam and Muslims ... The best thing, however, is if there are no Muslims left on our dear Earth."
In April, a Copenhagen suburban court found Paludan guilty of racism for comments directed at the spokeswoman of an ethnic group and was given a 14-day conditional jail sentence which he has appealed.
Three years earlier, he was convicted of insulting a police officer and told the court that he sustained a head injury in a 2005 accident after which "he found it very difficult to tolerate other people's mistakes without being very frustrated."
In 2013, he got a five-year restraining order for harassing a fellow student and, as a lawyer, he has been defending cases where asylum-seekers had their applications rejected.