Sometimes, it is possible that you only see a black screen after establishing a TeamViewer connection.
A black screen on the remote machine can have several reasons. Most of the cases it is due to the fact that
the TeamViewer service is not running correctly,
the connection is to a monitor-less computer or
there is something interfering/blocking the communication of TeamViewer.
In most cases you can already solve this problem by updating both sides of the connection to the newest release available within your major version.
In addition, there are following approaches:
restart the remote PC
completely close the remote TeamViewer including restarting the TeamViewer service (Start --> run --> services.msc)
Active RDP session
A black screen also appears, if there is an active RDP (Windows Remote Desktop) session on the remote computer with the RDP window currently being minimized. For a minimized RDP window the whole desktop is being minimized. Therefore, there is no possibility for TeamViewer to grab the screen of the remote computer.