Current leader Petro Poroshenko, 53, is seeking re-election but the surprise front-runner is 41-year-old comedian Volodymyr Zelenskiy.
Both, along with former PM Yulia Tymoshenko, 58, have expressed largely pro-EU views during the campaign.
None of the pro-Russian candidates are seen as serious contenders. Areas controlled by pro-Russian separatists are boycotting the poll.
If no candidate gets more than 50% on Sunday, the top two will fight it out in a second round on 21 April.
A total of 39 candidates are on the ballot paper, but only the three front-runners are considered to have any chance of victory.
The Ukrainian president has significant powers over security, defence and foreign policy and the ex-Soviet republic’s system is described as semi-presidential.
How did we get here?
Mr Poroshenko, one of Ukraine’s wealthiest oligarchs, was elected in a snap vote after former pro-Russian President Viktor Yanukovych was toppled in the February 2014 Maidan Revolution, which was followed by Russia’s annexation of Crimea and a Russian-backed insurgency in the east.
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The next president will inherit a deadlocked conflict between Ukrainian troops and Russian-backed separatists in the east, while Ukraine strives to fulfil EU requirements for closer economic ties.
The EU says that about 12% of Ukraine’s 44 million people are disenfranchised, largely those who live in Russia and in Crimea, which Russia annexed in March 2014.
Just who is the surprise front-runner?
Mr Zelenskiy is aiming to turn his satirical TV show – in which he portrays an ordinary citizen who becomes president after fighting corruption – into reality.
He has torn up the rule book for election campaigning, the BBC’s Jonah Fisher reports from Kiev. He has done no rallies and few interviews, and appears to have no strong political views apart from a wish to be new and different.
His extensive use of social media appeals to younger voters.
His readiness to speak both Russian and Ukrainian, at a time when language rights are a hugely sensitive topic, has gained him support in Ukraine’s largely Russian-speaking east.
Opinion polls suggest he will have a clear lead over Mr Poroshenko and Ms Tymoshenko in the first round, and would retain it in a run-off against either of them.
Who are the other candidates?
Mr Poroshenko aims to appeal to conservative Ukrainians through his slogan “Army, Language, Faith”.
He says his backing for the military has helped keep the separatists in eastern Ukraine in check. He also negotiated an Association Agreement with the EU, including visa-free travel for Ukrainians. During his tenure the Ukrainian Orthodox Church has become independent of Russian control.
However his campaign has been dogged by corruption allegations, including a scandal over defence procurement, which erupted last month.
The third main contender is Yulia Tymoshenko who has served as prime minister and ran for president in 2010 and 2014. She played a leading role in the 2004 Orange Revolution, Ukraine’s first big push to ally itself with the EU.
The front-runner among the pro-Russian candidates, Yuriy Boyko, says he would “normalise” relations with Russia.
