How do people arrive at new functional forms for models?

In my economics classes, when professors presented a new model they always started out by explaining the underlying assumptions, then presented the model's functional form. Over subsequent lectures we'd add new frictions/complications to the model to analyze different things.

My question is where does the functional form itself come from? Is it fully determined by the assumptions themselves? Is it based on some convention/tradition in the research community? Is it more art than science? I never thought about it at the time but it feels like a big hole in my knowledge–like there may be some "hidden assumptions" I'm not aware of.