IntroductionZeolites are tetrahedrally connected framework solids, based on silica, with intricate structures that possess channels and cages large enough to contain extra-framework cations and to permit the uptake and desorption of molecules varying from hydrogen to complex organics up to 1 nm in size. Their crystalline structure directly controls their properties and consequently their performance in applications such as ion exchange, separation, and catalysis, and is therefore of great interest to academics and technologists alike. A ''ball and stick'' representation of the most widely used zeolite A, with tetrahedral Al and Si atoms linked by O atoms and with chargebalancing Na + cations, is given in Figure 7.1.Originally discovered as aluminosilicate minerals, synthetic zeolites with a range of compositions are now widely prepared and subsequently modified for a wide range of applications. Many excellent articles, reviews, and books describe the structures of these solids, often in well-illustrated texts [1-3] and online resources [4]. Here we start by summarizing their structural chemistry, beginning with the key features of the best known and most widely used zeolites A and Y. Besides covering the periodic structures of these solids, other features such as secondary mesoporosity are also important to their performance and are discussed. This is followed by a summary of the structural chemistry of some of the important zeolite types prepared using inorganic and simple organic cations prior to the 1990s.Over the last 20 years there has been a major international effort to prepare new zeolitic materials, in the search for improved adsorbents and catalysts. Much of this has focused on the exploration of the use of complex organic alkylammonium ions, synthesized specifically as potential ''templates,'' giving high-silica-content zeolites or pure silica polytypes. The diversity of structures has also been increased by the inclusion of elements other than Al for Si in the framework, which may be either aliovalent (2+ or 3+) or isovalent (4+), and the search for new materials is encouraged by the tantalizing arrays of hypothetical structures that have been shown to be energetically feasible [5,6]. The remarkable products of this ongoing odyssey continue to show new structural features that are both intriguing and of practical importance or potential: increased crystallographic complexity leading to structures with novel