When quantum effects are small, Heisenberg antiferromagnets have a Néel ordered ground state, but strong zero-point fluctuations can lead to new ‘‘exotic’’ spin-liquid ground states without long-range Néel order. These effects are strongest in low dimensions and frustrated systems, and always occur in one dimension. The nature of the new ground state can depend on whether the microscopic spins have integer or half-integer S. As an example of such systems the rich phase diagram of the one-dimensional S=1 Heisenberg antiferromagnet with additional biquadratic exchange and uniaxial on-site anisotropy will be discussed in detail.