We describe a detailed study of the aluminum phosphate AlPO-53 in both its as-made and calcined forms. In its as-made state, AlPO-53(A), the material is templated by methylammonium cations and contains occluded water molecules and also hydroxide ions that bridge pairs of aluminum atoms, increasing their coordination number to 5. Solid-state NMR experiments confirm the local environment of the aluminum and phosphorus atoms proposed in a previous structural model from powder X-ray diffraction. P-31 NMR shows the presence of four distinct resonances with an intensity ratio of 1: 1:2:2, consistent with the expected six crystallographic p Sites. Al-27 triple-quantum MAS NMR resolves five aluminum peaks, two with NMR parameters characteristic of four-coordinate Al and three of five-coordinate Al. One of these latter signals has a greater intensity than that of the others, consistent with the presence of two overlapping signals from two distinct crystallographic Al sites. First-principles calculations of NMR parameters provide a complete spectral assignment and confirm our interpretation of unresolved spectra. AlPO-53(A) is found to convert easily into a second crystalline phase on moderate heating (upon spinning in the NMR rotor for an extended period, for example), and variable-temperature powder X-ray experiments, together with TGA, suggest that this is a dehydration process yielding a second aluminophosphate, JDF-2. This is confirmed using both P-31 and Al-27 NMR, with the spectral assignment of JDF-2 supported by first-principles calculations. Calcination of AlPO-53(A) or of the dehydrated material, JDF-2, at 300 degrees C yields the microporous open-framework material AlPO-53(B), a tetrahedral network with three Al and three P sites, as confirmed by NMR and first-principles calculations. In addition to demonstrating the power of the combined use of NMR, first-principles calculations, and diffraction for detailed structural investigations, we show that the possibility of a reversible dehydration in as-made AlPO-53 and similar systems is an important consideration in structural studies and provides evidence that the published structural model for AlPO-53(A) may be incomplete.