The CMS installer in Joomla! before 3.7.4 does not verify a user's ownership of a webspace, which allows remote authenticated users to gain control of the target application by leveraging Certificate Transparency logs.
In Joomla! 3.2.0 through 3.6.5 (fixed in 3.7.0), inadequate escaping of file and folder names leads to XSS vulnerabilities in the template manager component.