Magnets composed of molecular components that provide both electron spins and spin-coupling pathways can stabilize bulk magnetic ordering. This was first reported for the ionic, zero-dimensional (0-D) electron transfer salt [Fe(C₅Me₅)₂]⁺[TCNE]˙⁻ (TCNE = tetracyanoethylene), which orders as a ferromagnet at T_c = 4.8 K. Later V[TCNE]_x (x ∼ 2) was characterized to order above room temperature at 400 K (127 °C). Subsequently, numerous examples of organic- and molecule-based magnets have been characterized. In this critical review, after a discussion of the important aspects of magnetism pertaining to molecule-based magnets, including the determination of the magnetic ordering temperature (T_c) these magnetically ordered materials are reviewed from a perspective of the structural dimensionality (208 references).