In nature, animals need to adapt to constant changes in their environment. Learning and memory are cognitive capabilities that allow this to happen. Extinction, the reduction of a certain behavior or learning previously established, refers to a very particular and interesting type of learning that has been the basis of a series of therapies to diminish non-adaptive behaviors. In recent years, the exploration of the cellular and molecular mechanisms underlying this type of learning has received increasing attention. Hebbian plasticity (the activity-dependent modification of the strength or efficacy of synaptic transmission), and homeostatic plasticity (the homeostatic regulation of plasticity) constitute processes intimately associated with memory formation and maintenance. Particularly, long-term depression (LTD) has been proposed as the underlying mechanism of extinction, while the protein phosphatase calcineurin (CaN) has been widely related to both the extinction process and LTD. In this review, we focus on the available evidence that sustains CaN modulation of LTD and its association with extinction. Beyond the classic view, we also examine the interconnection among extinction, Hebbian and homeostatic plasticity, as well as emergent evidence of the participation of kinases and long-term potentiation (LTP) on extinction learning, highlighting the importance of the balance between kinases and phosphatases in the expression of extinction. Finally, we also integrate data that shows the association between extinction and less-studied phenomena, such as synaptic silencing and engram formation that open new perspectives in the field.