Taiwan's two main parties contesting the election are the ruling Democratic Progressive Party (DPP) and the Kuomintang (KMT).
The DPP has a majority in the 113-seat Parliament, with 68 seats. The KMT has 35 seats. Eight seats are held by two smaller parties and the remaining two by independents. The DPP favours Taiwan's formal independence, while the KMT, which ruled China before fleeing to Taiwan after being defeated by the Communists in 1949 in a civil war, favours close ties with Beijing.
In total, there are 45 parties standing in the parliamentary elections, mostly small groups with little hope of getting seats.
Three people are running for president: incumbent Tsai Ing-wen from the DPP, Kaohsiung Mayor Han Kuo-yu from the KMT, and Mr James Soong, who leads the small China-friendly People First Party.
The new president takes office on May 20. The presidential term is four years and a president can serve a maximum of two terms in a row.
The president is also commander-in-chief of the military, appoints the premier, who then forms a Cabinet, and signs legislation into law.
Polling stations are open from 8am to 4pm.
Taiwan media outlets will likely offer their predictions based on early vote counts on who has won in the early evening.
The losing candidates will concede defeat later in the evening, though that depends on how close the vote is or whether there is any dispute about vote numbers.
The Central Election Commission will announce the official results much later in the evening.
For the presidential election, the winner needs only a simple majority to win. There is no run-off election.
For Parliament, formally called the Legislative Yuan, each voter has two ballots, one for their local district candidate and the other for a party.
There are 113 seats in the Legislative Yuan, of which 73 are elected by simple majority in defined constituencies. Voters vote for a candidate in this case.
There are 34 seats "at large", allocated proportionally to each party. Voters vote for a party in this case. A party needs at least 5 per cent of the total party votes to win seats in the Legislative Yuan.
Six seats are reserved for Taiwan's aboriginal population.
The Legislative Yuan is the main lawmaking body, and members serve four years. New legislators will take office on Feb 1.
Some 19 million Taiwanese are eligible to vote out of a population of 23 million. Voters must be aged 20 and above.
During the last presidential and parliamentary elections in 2016, the turnout was around 66 per cent.