Open-framework inorganic and inorganic-organic hybrid materials constitute an important area of study in materials chemistry, because of their potential applications in areas such as sorption and catalysis. Besides aluminosilicate zeolites, the metal phosphates and carboxylates constitute large families of open-framework structures. The possibility of building open architectures with the sulfate and selenate anions as the basic building units has been explored in this thesis. Investigations of a variety of open-framework metal sulfates and selenates, as well as a family of jarosites of different transition metals are presented. More importantly, studies directed towards the synthesis and understanding of the magnetic properties of various Kagome compounds formed by the transition metal ions is discussed at length. After providing an introduction to inorganic open-framework compounds (Part 1), the thesis presents the results of the investigations of various transition and rare earth metal sulfates with diverse structures and dimensionalities in Part 2. Some of these compounds show interesting properties. For example, a two-dimensional Ni(II) sulfate exhibits ferrimagnetism whereas a three-dimensional Ni(II) sulfate with 10-membered channels is paramagnetic. A family of three-dimensional co-ordination polymers of Co(II) sulfate wherein the Co(II) sulfate layers are linked by diaminoalkanes of varying chain length has been synthesized and characterized. Organically-templated neodymium and thorium sulfates with layered and three-dimensional structure have also been prepared. The jarosite family of compounds with the Kagome structure is considered as an ideal model for studying frustrated magnetism. This type of materials, however, is difficult to prepare in a pure and highly crystalline form. We have synthesized analogues of the jarosite containing magnetic ions other than Fe3+ by solvothermal techniques and discussed them in Part 3. In particular, we have prepared and explored the magnetic properties of Mn2+(S = 5/2), Fe2+ (S = 2), Co2+(S = 3/2) and Ni2+ (S = 1) jarosites. Based on the results presented, it becomes clear that the magnetic properties vary with the spin of the transition metal ion. It appears that those Kagome compounds with transition metalions with non-integer spins show antiferromagnetic interactions and magnetic frustration while those with integer spins exhibit ferro/ferrimagnetic properties. A theoretical study has also supports this observation. We have been able to isolate for the first time 1,4-diazacubane as the part of the structure of the nickel Kagome compound. The possibility of building open architectures with the selenate anion as the basic building unit has been explored in Part 4. The results have been rewarding and an organically-templated three-dimensional lanthanum selenate with 12-membered channels has thus been obtained for the first time.