Are compliments applicable both to people and things, or to people only?
Macmillan specifically states that a compliment (the noun) is "something nice that you say to praise someone."
Oxford likewise asserts that to compliment (the verb) is to "politely congratulate or praise (someone) for something."
Other dictionaries (such as M-W) leave the definition open in an oddly truncated way: "to express esteem, respect, affection, or admiration to : to pay a compliment to."
By the last definition, one can compliment a thing, like the weather.