Choice between two possibilities.
We can either eat now or after the movie. It’s up to you. Would you like pork or fish? - Thanks, but I don’t like either of them.
Not either of the two things or people.
My parents live in Colombia, neither of the them lives in the USA.
Individual members of a group.
Each of us likes pizza. Each of the siblings has a different personality.
Refers to the entire group as a whole.
All of us agree with you. All of them are tired.
Neither of them is happy.
Each of them is smiling.
I don’t like either of them.
All of them are intelligent.