International Covenant on Civil and Political Rights

1st Optional Protocol to the Covenant

Convention on the Rights of the Child

Convention Against Torture and Other Cruel, Inhuman or Degrading Treatment or Punishment

Statute of the International Criminal Court (which excludes the death penalty)

Capital punishment is provided for 103 crimes: 19 crimes, including murder and espionage, under the constitution and 84 crimes under the National Security Law and five other laws. The National Security Law is a set of stringent strictures prohibiting even the vaguest expression of sympathy for communist North Korea.
Nobody has been executed since February 1998 when President Kim Dae-jung, who had been on death row himself, was sworn in.
The last execution was carried out in December 1997. Sixtyone people remained on death row with their death sentence finalized at the end of 2017 according to the press agency Yonhap.
In 2017 there was no new death sentence.
On 6 July 2015, 172 out of 298 lawmakers submitted a bipartisan bill to the National Assembly proposing to abolish the death penalty, citing a clause in the South Korean Constitution that obligates citizens to “respect human dignity.” “South Korea last carried out its last death sentence in December 1997. But the new draft bill aims to raise Korea’s status to an outright abolitionist country”, chief sponsor Rep. Yoo Ihn-tae of the main opposition New Politics Alliance for Democracy said, citing decades of efforts by human rights workers to have the practice outlawed here. “It is time we illegalize the death penalty here, in a country that has produced a U.N. secretary-general and is a member of the U.N. Human Rights Council,” Yoo added, referring to U.N. chief Ban Ki-moon. “It’s time that we declare the death penalty something that goes against our country’s conscience.” Lawmakers proposed six draft bills from 1999 to 2010 proposing to abolish the death penalty outright. But the draft bills failed to pass Korea’s unicameral parliament. Yoo’s proposed bill comes nearly five years after the last anti-death penalty bill was chiefly sponsored by lawmaker Joo Sung-young of the Grand National Party, a precursor to the ruling Saenuri Party, in November 2010.
The draft bill must pass the Legislation and Judiciary Committee and plenary voting at the National Assembly, before receiving final approval from the Cabinet for it to become law.
However, on 2 March 2016, the National Assembly passed a controversial anti-terror law that provides for the death penalty for any person found guilty of forming a "terror organisation". [see chapter “The War on Terror”].
On 6 November 2017, a poll was released by Realmeter and commissioned by local broadcaster CBS. It shows about one out of every two South Koreans is in favor of the death sentence. It has been conducted on over 500 adults, 52,8% of respondents supported executing death row inmates. 
 32% said capital punishment should be maintained but not be carried out while just over 9% said the death penalty itself should be abolished. Realmeter said that in a 2009 survey, 66% of respondents supported maintaining the death penalty while 21% wanted it scrapped. The pollster noted that people supporting abolishment are on the rise. The survey had a 95% confidence level with a margin of error of plus or minus four-point-three percentage points.

In 1996, the Constitutional Court ruled 7-2 that the death penalty was constitutional. In explanation of their decision, the Court said that the right to life can be restricted to safeguard innocent citizens. The Court also acknowledged the efficacy of the death penalty as a crime-deterrent.
On November 28, 2002, the Constitutional Court ruled as unconstitutional a clause in the National Security Law allowing the death penalty to be imposed on those found guilty of repeatedly praising North Korea, or encouraging others to do so.
On 8 September 2004, confirming a death sentence for murder, the Supreme Court ruled that the death penalty is justified for extremely inhuman crimes. "The decision means that those who commit brutal and inhuman crimes will not be considered a human being," said an official of the Court, adding that "in these cases, the death penalty is not go against the Constitution."
On 25 February 2010, the Court ruled again in favor of the death penalty, confirming the decision issued four years earlier. This time, however, the opinion of the court has been achieved with a minimum margin of 5 votes in favor and 4 against. According to the judges the society still requires profound changes before it is possible to abolish the death penalty.

The War on Terror
On 2 March 2016, despite a nine-day filibuster by 38 liberal members, the National Assembly passed a controversial anti-terror law that provides for the death penalty for any person found guilty of forming a "terror organisation". Following the end of the marathon filibuster, 156 members of the ruling Saenuri Party voted approval, while 1 opposed out of 157 present. Liberal parties such as Minjoo Party of Korea, Justice Party and People Party all left the house beforehand.
The anti-terror law was first proposed back in 2001 following the September 11 terror attacks. It had been put in motion multiple times since, but always failed to reach a vote due to strong opposition from NGOs and opposition parties.
The law defines terror as an "act that can put national security and citizens' safety at risk which includes the disturbance of the nation, regional government, and foreign government exercising its authority," which critics say is ambiguous and open to abuse.
The anti-terror law, once in effect, will give power to the National Intelligence Service (NIS) to collect data on terror suspects' private information, location, and IT use.
The Bill added new clauses for criminal prosecution: those who form a "terror organisation" can face capital punishment, life imprisonment, or over 10 years incarceration; those who plan an act of terror faces life imprisonment or over 7 years incarceration; and those who join a foreign terrorist group face over 5 years imprisonment.

United Nations
In November 2017, South Korea was revised under its third cycle of Universal Periodic Review. South Korea supported a general reccomendation to study the possibility of ratifying, among others international treaties, also the Second Optional Protocol but  merely noted recommendations to abolish the death penalty.

On 29 September 2017, South Korea abstained on the Resolution on the Death Penalty at the 36° session of the UN Council on Human Rights.
On 17 December 2018, South Korea abstained again on the Resolution on a Moratorium on the Use of the Death Penalty at the UN General Assembly.