Ancient cultures, such as the Romans, are known to have an equivalent of fast food restaurants: thermopolia. It seems reasonable to assume people could leave with their food if they wanted to.
I was curious if there was anything they had that was equivalent to, say, a Pizza box, or a paper wrapper for a burger.

I'm using the Romans as an example and would be interested to hear about equivalents in any non-modern culture, but particularly ones where something like cardboard or paper as we recognize it would not be available.

As an extra part to the question, if something like leaves were used, was there any particular plant that was favoured in these cultures?