Transition metal oxides form a large class of compounds that exhibit a very rich and diverse physics. This thesis involves a first-principles computational study of some transition metal oxides and their different physical properties. We study the emergence of ferroelectricity in Sr-Ti-O layered perovskites with strain, the microscopic mechanism of magnetodielectric coupling in EuTiO3 , and the structural trends of early transition metal dioxides with the Rutile structure. We explain and support the results of our first-principles calculations with physical models for each system.