Most are probably using cloud APIs. I've looked at AWS's before: https://aws.amazon.com/rekognition/content-moderation/. I'm sure there are a lot of them available. 

It should be fairly easy to run their own models too. This nsfw detecting model is the most popular image classifier on hugging face: https://huggingface.co/Falconsai/nsfw_image_detection

Looks like OpenAI can do it now: https://openai.com/index/upgrading-the-moderation-api-with-our-new-multimodal-moderation-model/

I am aware of the concept, but not aware of whether/which services are being used for this, and/or whether these are things developed in-house or with other types of automation providers.

BitcoinErrorLog

You haven't seen image feature detection? It's pretty common, e.g. "Does this image have a nipple in it?"