The magnetic properties are reported for three members of the glaserite series of compounds, Na2BaM­(VO4)2, M = Mn, Mn0.6Co0.4, and Co. Large single crystals are grown using a high-temperature hydrothermal synthesis method. This structure type exhibits a triangular magnetic lattice in which M2+O6 octahedra are interconnected with nonmagnetic (VO4)3– groups. All the structures crystallize at room temperature with rigid trigonal symmetry (space group P3̅m1); however, at lower temperatures both Na2BaMn­(VO4)2 and Na2BaMn0.6Co0.4(VO4)2 undergo a structural transition to lower symmetry (monoclinic, C2/c). The bulk magnetic measurements indicate that Mn- and Co-structures are antiferromagnetic and ferromagnetic, respectively. Na2BaMn0.6Co0.4(VO4)2 does not show any long-range ordering down to 0.5 K, although a broad heat capacity anomaly near 1.2 K suggests short-range magnetic order or freezing into a spin-glass-like state related to the chemical disorder and resulting competing magnetic interactions. The magnetic structures of Na2BaMn­(VO4)2 and Na2BaCo­(VO4)2 were determined using neutron powder diffraction. At zero magnetic field, Na2BaMn­(VO4)2 possesses an antiferromagnetic structure with the moments ordered in a Néel-type arrangement and aligned along the C4 axis of the octahedra. Under applied magnetic field at 0.3 K, the evolution of the magnetic structure toward a fully polarized state is observed. Na2BaCo­(VO4)2 represents a ferromagnetic (FM) magnetic structure with Co moments aligned parallel to the c-axis direction. The relationships between these structures and magnetic properties are discussed.