The cerebellum is an area of the brain that plays a crucial role in the learning of motor skills. This process involves climbing fibers, which provide teaching signals to Purkinje cells in the cerebellar cortex when perturbations occur during a movement. However, controversy has arisen over climbing fibers contribution to cerebellar learning. This is because climbing-fiber signals are described as "all-or-nothing": they fire a single burst of action potentials in response to all supra-threshold stimuli, regardless of their strength. On the contrary, motor learning is not all-or-nothing: the amount of learning is driven by the strength of perturbations. In this dissertation, I describe the experiments that I performed to unravel how climbing fibers may encode the strength of teaching signals. In Chapter 2, I present my behavioral studies in mice, which involved a simple cerebellar-dependent motor learning task, eyeblink conditioning. I show that mice take into account the strength of unexpected perturbations to adapt their movements trial-by-trial. In Chapter 3, I present a review of the previous literature and provide a hypothesis on how climbing fibers can encode the strength of teaching signals in a single trial. In Chapter 4, I present the findings of my in vivo two-photon calcium imaging experiments, which suggest climbing-fiber signals may not be all-or-nothing at the post-synaptic level. Finally, in Chapter 5 I describe the different mechanisms that we discovered for coding the intensity of teaching signals by Purkinje cells in the cerebellum of awake mice.