Two major institutions in Qatar that suffered major security attacks in the past 10 years are Qatar National Bank (QNB) and Qatar's News Agency (QNA)
• What did attackers break into?
In QNB's case, attackers bypased the database security system of the bank and leaked over 1.4 GB sensitive user information, such as account details, personal details, PINs and even credit card numbers.
In QNA's case, attackers gained access to the agency's website and official media accounts, publishing fake quotes attributed to the Emir of Qatar, Sheikh Tamim bin Hamad al Thani.
• How did the attackers break in?
In QNB's case, it is yet unclear if the attack was an inside job or an external attack, as the bank released no additional information. Thus, the mechanism used to breach QNB's system remains unknown.
In QNA's case, hacker's used a bug in the agency's website that allowed them to gain adminstratory priviliges.
• Who was impacted?
In QNB's case, thousands of users were affected by the data breach. Fortunately, by enforcing f2a authenification methods, the bank was able to prevent any money being stolen by the hackers, as they had no access to the physical devices of their victims.
In QNA's case, it is impossible to determine how many people were affected. The country suffered deeply after this attack, as some countries used the fake quotes as an excuse to form an illegal blockade on Qatar for over 4 years.
• How was it investigated?
QNB's policy is strongly against releasing any public comments or statements in such situations.
In QNA's case, a professional investigation team was formed in Qatar in order to determine the methods used by hackers in order to gain access to the social media accounts and websites. The team was able to quickly identify and fix the that bug allowed attackers to breach in.

Resources:
Cyberlands Article
Qatar's Government Communications Office Statement
Reuters