Neurons of the cerebellar nuclei generate the non-vestibular output of the cerebellum. Like other neurons, they integrate excitatory and inhibitory synaptic inputs and filter them through their intrinsic properties to produce patterns of action potential output. The synaptic and intrinsic features of cerebellar nuclear cells are unusual in several respects, however: these neurons receive an overwhelming amount of basal and driven inhibition from Purkinje neurons, but are also spontaneously active, producing action potentials even without excitation. Moreover, not only is spiking by nuclear cells sensitive to the amount of inhibition, but the strength of inhibition is also sensitive to the amount of spiking, through multiple forms of long-term plasticity. Here, we review the properties of synaptic excitation and inhibition, their short-term plasticity, and their influence on action potential firing of cerebellar nuclear neurons, as well as the interactions among excitation, inhibition, and spiking that produce long-term changes in synaptic strength. The data provide evidence that electrical and synaptic signaling in the cerebellar circuit is both plastic and resilient: the strength of IPSPs and EPSPs readily changes as the activity of cerebellar nuclear cells is modified. Notably, however, many of the identified forms of plasticity have an apparently homeostatic effect, responding to perturbations of input by restoring cerebellar output toward pre-perturbation values. Such forms of self-regulation appear consistent with the role of cerebellar output in coordinating movements. In contrast, other forms of plasticity in nuclear cells, including a long-term potentiation of excitatory postsynaptic currents (EPSCs) and excitation-driven increases in intrinsic excitability, are non-homeostatic, and instead appear suited to bring the circuit to a new set point. Interestingly, the combinations of inhibitory and excitatory stimuli that potentiate EPSCs resemble patterns of activity predicted to occur during eyelid conditioning, suggesting that this form long-term potentiation, perhaps amplified by intrinsic plasticity, may represent a cellular mechanism that is engaged during cerebellar learning.