I think some models support OTA updates. I want to say they aren't completely automatic, and you have to trigger them by issuing a modem command (the same way you control the modem in general). The modems expose a serial interface that you use to issue commands and see the result.
For the modem I have, MC7455, the updates are not OTA. You have to flash them manually. It's still a pretty easy process, though the last update caused a BSOD on Windows when it completed. But everything was updated and fine after that.
The modems often have 2 modes they can operate in, MBIM and QMI. MBIM I think is more established and has broader support in software, but I think is mostly a legacy/compatibility mode on the modems. QMI I think has lower overhead and is the protocol that they're moving towards. I believe it's a Qualcomm protocol.