The United States of America on Tuesday began voting to elect its 45th president, choosing between Democratic candidate Hillary Clinton and her Republican rival Donald Trump. Green Party candidate Jill Stein and Libertarian nominee Gary Johnson are also in the fray, besides vice presidential running mates Mike Pence for the Republicans and Tim Kaine for the Democrats.

Polling has begun in all states and Washington DC (formally known as the District of Columbia), with Hawaii being the last state to start voting. Polling data aggregator RealClear Politcs has placed Clinton on a 3.2-point lead on Trump.

Only a few small towns in New Hampshire had completed voting soon after midnight, as New Hampshire law allows communities with fewer than 100 voters to cast their ballots then. Clinton secured the first victory of the day, winning the New Hampshire village of Dixville Notch by four votes, according to The Telegraph. Trump secured two votes, while Johnson and 2012 Republican nominee Mitt Romney got one vote each.

Clinton and her husband, former US president Bill Clinton, entered the polling booth in Chappaqua, New York, amid cheers from supporters. Clinton later said voting for herself was "the most humbling feeling". "So many people are counting on the outcome of this election...I'll do the very best I can if I'm fortunate enough to win today," she said. Her running mate, Senator Kaine, voted in Richmond, Virginia, while Pence cast his ballot in Indianapolis.

Meanwhile, Trump said he would vote for himself. "Well, I've really worked on this hard," he said in an interview with Fox News. "I've decided to vote for Trump." The businessman said he and his party would "win a lot of states". "I mean, who knows what happens ultimately, but we're gonna win." The Republican nominee cast his vote at a polling booth in New York, close to Trump Tower, where two women protesting against him were arrested earlier in the day, according to The Guardian.

In Nevada, the Republican campaign alleged that elections officials in Clark County had "intentionally coordinated with Democratic activists" to rig the vote. The lawsuit claimed that the polling station had been allowed to remain open till late last week so everyone lined up to vote could cast their ballot. There have been no comments from the Democratic campaign or Clark County officials.

Polling stations had to switch to using paper ballots in a few states after voting machines faced technical snags. This lead to long queues at booths in North Carolina's Durham County and Utah's Washington County.

For Indian readers, the results are likely to become clear on the morning of Wednesday, November 9 (IST).

How the US presidential election works

To become president, a candidate needs to win at least 270 of the 538 votes of the "electors" of the electoral college, which is a body of people representing each state. Citizens, in actuality, are voting for the electors, who are either senior party or state officials. The number of electors in each state depends on the number of seats it has in the Senate and the House of Representatives.

The swing states hold the key to determining the outcome of the presidential elections. These are the states where neither party has a stark majority, but both enjoy similar popularity among voters. While Florida, Ohio and Pennsylvania are considered the major swing states this year, other crucial ones include New Hampshire, North Carolina, Colorado, Nevada, Wisconsin, Iowa and Michigan.

Besides voting to elect Barack Obama's successor, Americans are also electing all 435 members of the House of Representatives – the lower house of the US Congress – as well as one-third of the Senate. They are also voting for a number of local and state officials.

Pre-election day polls

A majority of the independent surveys conducted before the United States went to the polls showed Clinton leading Trump by a narrow margin. The CNN/ORC polls, which is based on viewers' opinions, said Clinton outperformed the businessman in all three presidential debates.

The Democrat, however, seemed to have lost a fraction of her popularity after the US Federal Bureau of Investigation announced on October 28 that it was opening a new investigation into the case involving her private email server. The agency gave her a clean chit in the case again on November 6, saying she was not guilty of any wrongdoing during her term as the US secretary of state.

RealClear Politics showed Clinton in the lead in every pre-election poll but two, one of which had her tied with Trump.

The campaign

Both campaigns leading to election day were marked by personal attacks and accusations. While Trump has accused his Clinton of misusing her official status, he has faced allegations of misogyny, racism, Islamophobia, sexual assault and threatening to commit war crimes.