Virtual orbitals are important in chemistry as they play a central role in molecular orbital theory. From a computational standpoint, orbital mixing between occupieds and virtuals determines the optimal occupied orbitals in mean-field Hartree-Fock theory and Kohn-Sham density functional theory. In wavefunction theory, electron correlation is typically described by amplitudes such as the pair correlations describing the simultaneous promotion of two electrons from occupied to virtual orbitals. The virtual orbitals span the unoccupied space, and the choice of representation is important. Canonical virtual orbitals are delocalized levels that are appropriate for electron attachment. Localized virtuals, such as the redundant non-orthogonal basis of atomic orbitals projected into the virtual space, permit development of efficient local correlation methods, because the amplitude tensors describing correlation become sparse. Other prescriptions for localized orthogonal virtuals exist, as well as proposals to form sets of virtuals that are specifically optimized for correlations that involve a given occupied level, as will be discussed below.