Nuclear fusion in heavy-ion collisions is a dynamical process of quantum many-body systems. Heavy ion fusion studies have attracted researchers not only for the cause of energy production in the stellar region but also for the formation of new exotic nuclear isotopes. Great progress in synthesizing new heavy and superheavy nuclei by these types of nuclear interactions has been achieved in recent years. They can also provide useful information regarding the nuclear structure and interaction potential of the colliding nuclei. Theoretically, the simplest approach for heavy-ion fusion reactions is to use the one-dimensional potential model where both the projectile and the target are assumed to be structureless. The single-barrier penetration models have been applied to describe successfully the capture cross sections for light reaction systems around and above the Coulomb barrier region. However, sub-barrier fusion in heavy ion-induced reactions offers possibilities to explore static and dynamic properties of nuclei and to investigate the advancement of tunneling phenomena in terms of couplings of inelastic excitations and transfer channels. In this lecture, we try to present some of the recent developments in heavy ion fusion reactions.