How to containerize apps?

There are a lot of Android apps out there that request all sorts of permissions. They want access to your files, your contacts, etc. Many of them don't run properly and/or crash without these permissions. Is there a way of installing and running these apps without exposing information? Can I "containerize" apps, where it is still granted permissions but runs in a sandbox/container where my personal information isn't visible? The usual way for me to do this on a computer is to run the app in a virtual machine, but VMs are not available on Android. Alternatives?