Applies to: Mac PC running Mojave 10.14 OS or higher.
Prerequisites: None.

How to control a Mac running
macOS 10.14 or higher:

Apple has introduced a security mechanism with macOS 10.14 (Mojave), which requires special access to be granted to remote control applications like TeamViewer.

And macOS 10.15 (Catalina) has strengthened the security and privacy even further and requires additional permissions to be given to TeamViewer in order to control your Mac.

Without this access, TeamViewer users connecting to macOS 10.14 or higher will only be able to view the screen but not control it with their mouse or keyboard.

📌Note: TeamViewer is not able to grant this access by itself, nor can the access be granted remotely through a TeamViewer connection from another computer.

How to grant access to TeamViewer on your Mac

If you're starting TeamViewer 14 or higher on your Mac running macOS 10.14 (Mojave) or higher for the first time, you will be prompted with the following dialog:

By default, all permissions are set to Denied. Please give permission to the system capabilities manually to use TeamViewer as desired. If you or others need to access the Mac remotely, Screen Recording and Accessibility are required at a minimum.

To allow the access, click the buttons shown in the dialog. Click to allow Accessibility, click on Request Access -  then click on Open System Preferences

which will bring you to the Accessibility section of the Privacy panel,
inside the Security & Privacy preferences:

For the Accessibility access, you will need to click the padlock icon in the lower-left corner to make changes. You might be prompted to enter the credentials of an administrator account to continue.

Put a check next to TeamViewer to grant it access:

Repeat the same for Full Disk Access and Screen Recording. 
Those are required to control your Mac.

Click again on the padlock in the lower-left corner to prevent further changes.

Once you have done it for every category, you can close the Security & Privacy window. The next time you want to receive an incoming connection with TeamViewer, the person connecting to your Mac will be able to see and control your device.