In an antiferromagnet, adjacent spins want to point opposite. On a triangular lattice, this is impossible: if two spins are antiparallel, the third must be parallel to one of them — the system is geometrically frustrated. Unlike square lattices which order perfectly into a Néel state, the triangular antiferromagnet has a highly degenerate ground state manifold, leading to no long-range order even at T=0 and exotic spin-liquid behavior.