Classical measurement strategies in many areas are approaching their maximum resolution and sensitivity levels, but these levels often still fall far short of the ultimate limits allowed by the laws of physics. To go further, strategies must be adopted that take into account the quantum nature of the probe particles and that optimize their quantum states for the desired application. Here, we review some of these approaches, in which quantum entanglement, the orbital angular momentum of single photons, and quantum interferometry are used to produce optical measurements beyond the classical limit.