Vita:SD2Vita
The SD2Vita, based on research by motoharu and xyzz but launched in July 2017 by Gadorach, is a mechanical adapter to connect an ordinary microSD card to the system's gamecard slot (also based on the MultiMediaCard although only at an electrical level).
Variants
It launched as a bare PCB (available in multiple colors) to be wedged into the slot without engaging the eject spring, then a slightly shortened version was made to allow the cover flap to close reliably on all models. Then "packaged" versions with a proper plastic shell, compatible with the console's push-push eject mechanism, started appearing and became ubiquitous in a variety of designs, including one in the style of generic microSD to Memory Stick converters; for the most part they are all equivalent, with [lack of] quality control playing a bigger role in variation between samples.
For the same reason, little should be read into the "version number" they are sometimes prominently advertised with.
Software
Third party software is required to actually mount the SD2Vita as a storage device.
By convention, the card should be formatted directly (i.e. in superfloppy mode, without a partition table) as exFAT.
GameSD
The original plugin by xyzz with no configuration: it just mounts the device as ux0 if it can.
https://github.com/xyzz/gamecard-microsd/releases
GameSD_UO
A mod of GameSD that mounts the card as secondary storage (uma0). Abandoned and only compatible with 3.60.
https://vitadb.rinnegatamante.it/#/info/313
VitaShell
VitaShell has a built in way of mounting an SD2Vita as primary storage (ux0).
VitaDeploy
VitaDeploy has built in way of mounting
StorageMgr
A newer plugin by CelesteBlue, allowing to assign a mountpoint to any supported device (SD2Vita, USB storage, memory card, internal virtual memory card partition).
https://github.com/CelesteBlue-dev/PSVita-StorageMgr/releases
YAMT (Recommended)
Yet Another Mount Tool is the newest plugin that allows for management of the PS Vita's storage partitions, and comes pre-installed with VitaDeploy's recommended plugins. It also supports the SD2Vita and psvsd, although it has poor functionality with the psvsd so it is recommended to use StorageMgr with it instead.