I have understood that many poetic meters were inherited to Latin from the Greeks. This includes, for example, the dactylic hexameter and the Sapphic meters. But the Romans did have their own poetic forms before adopting anything from the east. The only thing I know of is the Saturnian. I do not know much about the history of metric poetry, but I would like a brief overview of the Greek influence on Latin poetry: How do the poetic forms of Greek origin differ from Latin ones? What, at a high level, changed in Roman poetry due to Greek influence? Is there a difference in the way of viewing, structuring or reading poetry that captures the spirit of this transition?
There is no need to give a full account if it would be long. Instead, an overview with citations of further reading or ideas for more detailed questions would be nice.