The ability to control how we process information by remembering that which is important and forgetting that which is irrelevant is essential to maintain accurate, up-to-date memories. As such, memory success is predicated on both successful intentional encoding and successful intentional forgetting. The current study used an item-method directed forgetting paradigm to elucidate the cognitive and neural processes that underlie both processes while also examining the relationship between them to understand how the two may work together. Results indicated that encoding-related processes in the left inferior PFC and medial-temporal lobe (MTL) contribute to subsequent memory success, whereas inhibitory processes in the right superior frontal gyrus and right inferior parietal lobe contribute to subsequent forgetting success. Furthermore, connectivity analyses found a negative correlation between activity in the right superior frontal cortex and activity in the left MTL during successful intentional forgetting but not during successful encoding, incidental forgetting, or incidental encoding. Results support the theory that intentional forgetting is mediated by inhibition-related activity in the right frontal cortex and the interaction of this activity with that of encoding-related activity in the MTL. Further support for this inhibitory-related account was found through a clear dissociation between intentional and incidental forgetting, such that intentional forgetting was associated with regions shown to support inhibition, whereas incidental forgetting was associated with regions supporting encoding.