Ubuntu 18.04 alt+shift+tab does not switch apps backwards

That's because Alt+Shift+Tab in Ubuntu 18.04 is blocked by another shortcut.

Run this command to free the Alt+Shift combination:

gsettings reset org.gnome.desktop.input-sources xkb-options

source1 source2

I was able to resolve it using Gnome Tweaks GUI.

Open Tweaks and go to Keyboard & Mouse, then click - Additional Layout Options: as shown here, ans then uncheck Alt+Shift under Switching to another layout section as shown here

That fixed it for me.

I use Ubuntu 18.04 with KDE and the answer from dima.rus helped me diagnose the problem: it was caused by a conflict with the shortcut for keyboard language switching.

What solved the problem for me:

1. Change the Main shortcuts in System Settings -> Keyboard -> Layouts -> Shortcuts for Switching Layout which was Alt+Shift. EDIT: Do not set it to the otherwise rarely used Caps Lock as once I mapped and started using it, in some rare cases it caused the keyboard caps lock mode getting enabled and stuck (as indicated by the keyboard's caps lock light indicator), and forced me to reboot. EDIT: or instead of reboot, just start Onboard (the KDE on-screen keyboard) and use it to press Caps Lock virtually.
2. Set the Reverse to Alt+Shift+Tab in System settings -> Task Switcher -> Main -> Visualization -> Shortcuts
3. Log out and in again to KDE