Open-framework inorganic materials constitute an important area of study in materials chemistry, because of their potential applications in areas such as sorption and catalysis. After the discovery of nanoporous aluminium phosphates by Flanigen et al in 1982, there has been a tremendous growth in the area of porous solids. Most of them are based upon oxygen containing materials especially phosphates, and they exhibit fascinating architectures with unusual bonding and coordination environment. Besides metal phosphates and phosphites, inorganic-organic hybrids constitute an important family of open-framework structures. In this thesis, results of investigations of a variety of open-framework metal phosphates, metal phosphites, as well as a new family of phosphite-oxalates are presented. More importantly, studies directed towards the synthesis and understanding of the magnetic properties of various transition metal phosphates, phosphites, phosphite-oxalates and the upconversion behavior of uranium phosphites are discussed at length. In Chapter 1 of the thesis an overview of inorganic open-framework materials is presented. In Chapter 2 and 3, the synthesis, structure of open-framework zinc (Part A of both Chapters) and synthesis, structure and magnetic properties of open-framework iron (Part B of both Chapters) are presented. Some of these compounds show unusual structure and interesting properties. For example, two-dimensional iron phosphate exhibits ferrimagnetism whereas three-dimensional iron phosphate with SBU-6 and SBU-2 is antiferromagnetic. The three-dimensional iron phosphite exhibits small polarization at low field. In Chapter 4, we present a new family of organically templated hybrid materials synthesized by partially substituting the phosphite by the oxalate ion in manganese, iron and cobalt phosphites. These exhibit a wide range of structures in which the oxalates play an unusual dual role. Some of these compounds show interesting magnetic properties. For example, manganese phosphite-oxalate shows magnetic polarizations on application of high field at low temperatures and iron phosphite-oxalate exhibit ferromagnetism at very low temperature. While a large number of organically templated transition and main-group element phosphites have been synthesized, research on lanthanide and actinide phosphites has been rare. Most of the reported open-framework phosphate and phosphite compounds of uranium possess uranium in +6 oxidation state. The possibility of building open architectures of uranium phosphites has been explored in Chapter 5. The results have been rewarding and both layered and three-dimensional structures have been prepared. Two of them contain uranium in +4 state and exhibit upconversion behavior.