In this work, an extensive simulation study of the cerebellum is presented. Our study required the further development of the EDLUT spiking neural network simulator. Thus we have addressed the development of a detailed cerebellar model from different levels of abstraction. Firstly, in a detailed model, the granular-layer network generated rebounds and oscillations in the β/γ-frequency band and filtered unsynchronized trains with millisecond precision. We found that weights at multiple synapses could play a crucial role to enhance coincidence detection (which allows the reduction of non-synchronous signals) and sensitivity rebound (which determines specific time windows for signal transmission). These results predict that the granular layer operates as a complex adaptable filter which can be controlled by weight changes at multiple synaptic sites. In a higher level of abstraction, a model of the whole cerebellum which can infer corrective models in the framework of a control task is presented. This work studies how a basic temporal-correlation kernel, including long-term depression (LTD) and long-term potentiation (LTP) at parallel fibers-Purkinje cell synapses, can effectively infer corrective models. Finally, we study how cerebellar input representations (context labels and sensorimotor signals) can efficiently support model abstraction towards delivering accurate corrective torque values for increasing precision during different-object manipulation.