Are you able to use a custom Postgres comparison function for ORDER BY clauses?

In Python, I can write a sort comparison function which returns an item in the set {-1, 0, 1} and pass it to a sort function like so:

sorted(["some","data","with","a","nonconventional","sort"], custom_function)

This code will sort the sequence according to the collation order I define in the function.

Can I do the equivalent in Postgres?

e.g.

SELECT widget FROM items ORDER BY custom_function(widget)

Edit: Examples and/or pointers to documentation are welcome.