Insert, on duplicate update in PostgreSQL?

Several months ago I learned from an answer on Stack Overflow how to perform multiple updates at once in MySQL using the following syntax:

INSERT INTO table (id, field, field2) VALUES (1, A, X), (2, B, Y), (3, C, Z)
ON DUPLICATE KEY UPDATE field=VALUES(Col1), field2=VALUES(Col2);

I’ve now switched over to PostgreSQL and apparently this is not correct. It’s referring to all the correct tables so I assume it’s a matter of different keywords being used but I’m not sure where in the PostgreSQL documentation this is covered.

To clarify, I want to insert several things and if they already exist to update them.

Insert, on duplicate update in PostgreSQL?