Pi-hole through 5.0 allows code injection in piholedhcp (the Static DHCP Leases section) by modifying Teleporter backup files and then restoring them. This occurs in settings.php. To exploit this, an attacker would request a backup of limited files via teleporter.php. These are placed into a .tar.gz archive. The attacker then modifies the host parameter in dnsmasq.d files, and then compresses and uploads these files again.
The Gravity updater in Pi-hole through 4.4 allows an authenticated adversary to upload arbitrary files. This can be abused for Remote Code Execution by writing to a PHP file in the web directory. (Also, it can be used in conjunction with the sudo rule for the www-data user to escalate privileges to root.) The code error is in gravity_DownloadBlocklistFromUrl in gravity.sh.