Is monogamy a natural state of affairs ?

Is monogamy actually natural, or is it mostly a social and moral construct?
Humans have a biological drive to reproduce, seek novelty, and potentially spread their genes, especially in the male. Yet humankind can also form deep bonds, raise children together, and value loyalty and commitment.
So what is monogamy really: our natural state, a social invention, or a compromise between biological instinct and the kind of society we want?
And if biology pulls one way while morality pulls another, which should we follow?