This Account describes a family of aluminophosphates ranging from neutral open-frameworks to anionic frameworks with fascinating structural architectures. In contrast to aluminosilicate zeolites, these aluminophosphates exhibit wealthy structural features, including extra-large micropores, mixed bonding, different structural dimensionalities, rich compositional diversities, and various stacking sequences of their 2-D sheets. The low-dimensional networks, acting as building units, can be assembled to 3-D open-frameworks via transition metal cations through a building-up process. New stoichiometries and hypothetical structural topologies can be predicted and enumerated. Computational and combinatorial approaches will greatly help to access the range of the diverse structures.