How to create Material UI Dialog with transparent background color?

For the latest version ("@material-ui/core": "^1.2.3"), here is how it’s done:

<Dialog
  {...otherProps}
  PaperProps={{
    style: {
      backgroundColor: 'transparent',
      boxShadow: 'none',
    },
  }}
>
  {/* ... your content ... */}
</Dialog>

Take note of the new PaperProps prop. It’s not in the documentation but if you check out the source, they are using PaperProps as one of the props you can pass in – since this isn’t in the docs, this might change with future versions though, so be careful here.