Marcel Pociot, author of the excellent BotMan package, published a post on how he used Custom Elements for VueJS to power a widget that users can embed on their sites.

I am currently in the middle of working on a new BotMan feature - a frontend widget that you can embed into your website to make it easier to connect your website visitors with your own self-hosted chatbot solution. The backend / PHP side is already working and leverages the BotMan web driver, which is basically just an API that you can use to interact with your chatbot.