How to use "than"

[Yxr]

For my understanding that "than" can be a conjunction as well as a preposition.

Could somebody tell me when it is used as a conjunction or preposition?

In the following examples, which is correct?

She is older than I.
She is older than I am.

Thanks

[Mister Micawber]

She is older than I.-- Correct, but nowadays sometimes considered hypercorrect.
She is older than I am.-- Correct
She is older than me. -- Correct, but sometimes still considered overly casual.
_________________
Native English teacher at Mister Micawber's

[Yxr]

Thanks