There are quite a number of mass storage devices now available for the BBC Micro using modern hardware. Many of them use flash memory cards, like SD, MMC and Compact Flash cards.

Here is another example of an MMC storage device, which connects to the Beeb's user port, and apparently is controlled by a patched version of the BBC DFS, but I didn't quite get round to looking into that at Console Combat. Here's a picture of what it looks like anyhow.