Proving the existence of God is a perennial philosophical ambition. An armchair proof would be the jackpot. Ontological arguments promise as much. This Element studies the most famous ontological arguments from Anselm, Descartes, Plantinga, and others besides. While the verdict is that ontological arguments don't work, they get us entangled in fun philosophical puzzles, from philosophy of religion to philosophy of language, from metaphysics to ethics, and beyond.