Mobile: How to download files and Apps now?

A key advantage of Android compared to Iphone used to be the ability to handle files (download and Bluetooth).

However, recently both my Androids have complained storage is low.
One has 2 GB of Android hidden files, the other 4 GB.
Less about 200 MB for downloads!

Now that Android is making it impossible to do downloads (I do have a SD card, but Chrome doesn't seem to have heard of them), what options are available?

Drop Android and use a PC?

I had same problem with my Xperia sp. I had to reset my phone to clear memory.