Prosecutors, the police and the Corruption Investigation Office for High-ranking Officials have all launched probes into Yoon and the officials, seeking to pursue charges of insurrection and abuse of power, among others.
Here is what we know about the investigations so far:
WHO IS UNDER INVESTIGATION?
Besides Yoon, his former defence minister Kim Yong-hyun, former interior minister Lee Sang-min and army chief Park An-su, who was named martial law commander, face investigations.
Others involved in the case include the chiefs of the Capital Defence Command, the army's Special Warfare Command and the Defence Counterintelligence Command, as well as several other military generals and senior police officials, including the national and Seoul police chiefs, who are accused of playing a role in the martial law plan.
The main opposition Democratic Party said on Monday that it has also filed a complaint against Prime Minister Han Duck-soo to be included in the investigations for failing to block Yoon's attempt at martial law.
Yoon, Kim, Lee, the national and Seoul police chiefs and 10 military commanders have been banned from leaving the country.
Prosecutors summoned Kim for questioning for a third time on Monday since arresting him a day before, and carried out raids of the Defence Counterintelligence Command's headquarters and offices nationwide, according to the Yonhap news agency.
Police also raided the defence ministry and the Capital Defence Command on Thursday, seeking to seize Kim's secure phones and related materials, Yonhap said.
WHO LEADS INVESTIGATIONS?
The Supreme Prosecutors' Office has created a special investigation bureau to examine the case for the first time since it probed a 2016 corruption scandal engulfing then-President Park Geun-hye, who was impeached and eventually ousted.
It consists of some 50 prosecutors and investigators, and about a dozen military prosecutors have also been drafted in, Yonhap said.
The chief of investigations for the national police agency also confirmed the launch of its investigation at a parliamentary hearing on Thursday, and Yonhap said its team would include some 150 officers and investigators.
The Corruption Investigation Office for High-ranking Officials (CIO) said it had separately opened an investigation after receiving complaints about national police chief Cho Ji-ho and other senior police officials.
Amid growing concerns about signs of rivalry among probing agencies and calls for concerted efforts to prevent overlaps and boost effectiveness, a joint investigation team was launched on Wednesday between police, the CIO and the defence ministry.
CIO head Oh Dong-woon said on Wednesday that talks with prosecutors were under way on how to integrate their work but any quick conclusion appeared unlikely.
The parliament passed bills this week for the appointment of special counsels to spearhead a collective investigation with support from other agencies.
WHAT CHARGES ARE SOUGHT?
The officials face potential charges of insurrection, abuse of authority and obstructing other people from exercising their rights.
If convicted, the crime of leading an insurrection is punishable by death or life imprisonment, with or without prison labour. For those who participated in an insurrection plot or engaged in other essential activities punishment could range from death to life imprisonment down to imprisonment without prison labour for at least five years. People who merely joined in the plot or violence face imprisonment, with or without prison labour, for less than five years.
Abuse of authority brings penalties of imprisonment for less than five years or fines of up to 10 million won ($7,000), while obstructing other people's rights is punishable by a prison term of less than five years or fines of up to 7 million won.
South Korea last handed down a death sentence in 2016, but has not executed anyone since 1997.
