The authors consider the results of experimental investigations of garnets in which antiferromagnetic ordering occurs because of the weak exchange interaction within one of the sublattices: dodecahedral, octahedral, or tetrahedral. They discuss the characteristics of magnetic phase transitions in rare-earth gallates and aluminates, whose magnetic properties are described by the Ising model of an antiferromagnet with allowance for the effects of the crystalline field. They analyze the magnetic phase diagrams and critical behavior of garnets with rare-earth ions in dodecahedra. They describe the magnetic characteristics of garnets containing $3d$ ions and consider the peculiarities of their behavior in an octahedral crystalline field. Taking the magnetic structure into account, they analyze antiferromagnetic exchange interactions in the garnet structure and the results of experimental study of the specific heat and of antiferromagnetic resonance in the spin-flop state of garnets with magnetic ions in octahedra. It is shown that the magnetic properties of these compounds are well described in the molecular-field approximation. Finally, magnetic structures and exchange interactions are discussed for antiferromagnetic garnets whose tetrahedral sublattice is formed by Fe$^{3+}$ ions.