File-based dynamically-allocated hard-disk on Linux

I can create a regular file on an existing file-system (say, ext4), make it into a block device (via losetup), and format it with an ext4 file-system of its own.

But the above hard-disk is of a fixed size.

Question:

1. VirtualBox allows you to create VDI, VMDK, and VHD types of hard-disks that can be either fixed- or dynamically-sized. Is there any way to make a file-based dynamically-sized hard-disk for use by a Linux host OS?

2. Is it possible to employ any of these three types of file-based, dynamically-sized hard-disks outside of VirtualBox, on a Linux host OS?

I'm on Ubuntu 16.04.