A comprehensive study of the influence of classical anisotropy fields on the magnetic properties of Heisenberg antiferromagnets within unified molecular field theory versus temperature T , magnetic field H , and anisotropy field parameter h A 1 is presented for systems comprised of identical crystallographically-equivalent local moments. The anisotropy field for collinear z -axis antiferromagnetic (AFM) ordering is constructed so that it is aligned in the direction of each ordered and/or field-induced thermal-average moment with a magnitude proportional to the moment, whereas that for XY anisotropy is defined to be in the direction of the projection of the moment onto the x y plane, again with a magnitude proportional to the moment. Properties studied include the zero-field Néel temperature T N , ordered moment, heat capacity, and anisotropic magnetic susceptibility of the AFM phase versus T with moments aligned either along the z axis or in the x y plane. Also determined are the high-field magnetization perpendicular to the axis or plane of collinear or planar noncollinear AFM ordering, the high-field magnetization along the z axis of a collinear z -axis AFM, spin-flop (SF), and paramagnetic (PM) phases, and the free energies of these phases versus T , H , and h A 1 . Phase diagrams at T = 0 in the H z − h A 1 plane and at T > 0 in the H z − T plane are constructed for spins S = 1 / 2 . For h A 1 = 0 , the SF phase is stable at low field and the PM phase at high field with no AFM phase present. As h A 1 increases, the phase diagram contains the AFM, SF, and PM phases. Further increases in h A 1 lead to the disappearance of the SF phase and the appearance of a tricritical point on the AFM-PM transition curve. Applications of the theory to extract h A 1 from experimental low-field magnetic susceptibility data and high-field magnetization versus field isotherms for single crystals of AFMs are discussed.