I'm using Gnome Shell.
Alt+Tab shows all opened application windows from all virtual desktops. It becomes impossible to use when many windows are opened. Is it possible to show only these apps which are on active desktop?
One potential option you may wish to consider is the Gnome-Shell Alternate Tab extension
It is the traditional Window-based Alt-Tab switcher that Ubuntu users have grown up with.
It doesnt meet your question "active desktop" criteria - however it does make switching more obvious and easier when you have multiple windows opened.
It is packaged in a PPA
As with all PPAs - these are testing for testing purposes. Either have a full backup you can restore with or use
Two ways to solve the problem.
There is a Gnome Shell extension that does this: Alt Tab Workspace.
You could also directly enable this behavior in the default switcher by running:
which is what the extension does under the hood.