Alt + Shift to change language no longer working after upgrade to Windows 10
Solution 1:
Go to Control Panel\Clock, Language, and Region\Language\Advanced settings, in a section called Switching input methods click on Change language bar hotkeys, continue with Advanced key settings tab, then click on button Change Key Sequence... and then choose from a list called Switch Keyboard Layout your desired LEFT ALT + SHIFT hotkey.
Solution 2:
The question is quite old. However, there is a common misunderstanding of the language concept of Windows 10 in the question. The concept also was not captured by any of the answers.
Meaning of the shortcuts
Alt + Shift changes the language, if I have defined different languages as described below.
Windows + Space changes the keyboard layout within the currecntly selected language, if I have defined different keyboards as described below.
Background
In Windows 10, there is a difference between language and keyboard layout.
In the language config window, one can choose the prefered language (see screenshot below; sorry for the German system language). E.g. the MS Word spelling correction is automatically adapted to the current language.
For each language, the user may define one or more keyboard layouts. First, the user clicks onto the language (next picture) and, then, she can choose "Optionen" ("Options" in English GUI?).
In the language options windows, the user can add different keyboard layouts. Swichting a keyboard layout does not impact app behaviour with respect to its language settings.
For each language one can define an individual set of keyboard layouts.
Which language and keyboard layout are selected?
Below are two screenshots of my Windows 10 taskbar. The top row in each picture indicates the system language (German ("DEU") in my case). The bottom row indicates the keyboard layout (German in the first and US-English in the second picture).
If there is only one row, it indicates the system language with default keyboard. Please correct me, if I am wrong with this.
Solution 3:
For me this worked (Late Answer, but I hope it will be helpful for future visitors):
Search for Setting --> Time & Language --> Language
Spelling, typing, & keyboard settings --> Advanced keyboard settings
Language bar options
Advanced Key Settings --> Between input languages --> Change Key Sequence --> Left ALT + Shift
You can also search for Advanced keyboard settings
directly and make your way shorter.