This book deals with some of the recent as well as traditional problems in nuclear structure physics originating from various nuclear models. It introduces the recent developments in nuclear theories such as effective relativistic mean field theory and non-relativistic Skyrme-Hartree-Fock approach. The main features of these theories used in this present work are in microscopic level, that deals with a wide range of nuclear systems ranging from light to heavy and superheavy nuclei including proton to neutron drip-lines. Special emphasis is given to the fundamental nucleon-nucleon interactions in relativistic mean field theory, in terms of the meson masses and their coupling constants. Investigations are also done for finding the Island of stability and the alpha decay half-life for superheavy valley. Moreover, the various decay modes including the rare event as cluster decay are taken into account for discussions.