In this account, a new concept of ''sponge crystals'' is presented on the basis of new interpretation of our previous results of porous heteropolyacids, that is, porous aggregates of self-assembled (NH 4 ) 3 PW 12 O 40 nanocrystallites (Ito, Inumaru, and Misono, J. Phys. Chem. B 101 (1997) 9958; Chem. Mater. 13 (2001) 824) ''Sponge crystals'' are defined as single crystals having continuous voids within them, but unlike zeolites, no intrinsic structural pores. This new category includes molecular single crystals having continuous voids originating from series of neighboring vacancies ( ‡1 nm) of the constituent large molecules, affording nanospaces in the crystals. A typical example of ''sponge crystals'' is (NH 4 ) 3 PW 12 O 40 , which is formed via the dropwise addition of ammonium hydrogen carbonate into an H 3 PW 12 O 40 aqueous solution (titration method) at 368 K. The resulting (NH 4 ) 3 PW 12 O 40 nanocrystallites (ca. 6-8 nm) then self-assemble with the same crystal orientation to form porous dodecahedral aggregates in the solution. During the formation process, necks grow epitaxially between the surfaces of the nanocrystallites (''Epitaxial SelfAssembly'') to form aggregates of which each aggregate has an ordered structure as a whole single crystal. Although the crystal structure of (NH 4 ) 3 PW 12 O 40 has no intrinsic structural(''built-in'') pores, X-ray diffraction, electron diffraction and gas adsorption experiments all reveal that each (NH 4 ) 3 PW 12 O 40 aggregate is comprised of a single crystal bearing many micropores. These pores are considered to be continuous spaces as neighboring vacancies of the molecules (anions and cations) originating from the residual spaces between the self-assembled nanocrystallites. The porous (NH 4 ) 3 PW 12 O 40 single crystals are considered a special case of ''mesocrystals,'' as was recently discussed by Co¨lfen and Antonietti (Angew. Chem. Int. Ed. 44 (2005) 5576). In contrast to most ''mesocrystals,'' which are generally polycrystalline in nature, each aggregate of (NH 4 ) 3 PW 12 O 40 is a characteristic porous single crystal. Furthermore, the micropores of (NH 4 ) 3 PW 12 O 40 are totally different from those found in other microporous crystals: zeolites have ''built-in'' pores defined by their crystal structure, while the (NH 4 ) 3 PW 12 O 40 nanocrystallites have none. Since (NH 4 ) 3 PW 12 O 40 micropores are continuous spaces as neighboring vacancies of the molecules, the shapes of the (NH 4 ) 3 PW 12 O 40 pores can in principle, assume various connectivities or networks within the crystal, and as such, are subsequently termed: ''sponge crystals.''