At variance with structural ferroic phase transitions which give rise to macroscopic tensors coupled to macroscopic fields, criteria defining antiferroelectric (AFE) phase transitions are still under discussion due to the absence of specific symmetry properties characterizing their existence. They are recognized by the proximity of a ferroelectric (FE) phase induced under applied electric field, with a double hysteresis loop relating the induced polarization to the electric field and a typical anomaly of the dielectric permittivity. Here, we show that there exist indeed symmetry criteria defining AFE transitions. They relate the local symmetry of the polar crystallographic sites emerging at an AFE phase transition with the macroscopic symmetry of the AFE phase. The dielectric properties of AFE transitions are deduced from a Landau theoretical model in which ferroelectric and ferrielectric phases are shown to stabilize as the result of specific symmetry-allowed couplings of the AFE order parameter with the field-induced polarization.