Climbing fiber (CF) activation evokes a large all-or-nothing electrical response in Purkinje cells (PCs), the complex spike. It has been suggested that the role of CFs (and thus complex spikes) is that of a "teacher" in simple learning paradigms such as associative eyeblink conditioning. An alternative hypothesis describes the olivocerebellar system as part of a timing device and denies a role of the CF input in learning. To date, neither of these hypotheses nor others can definitively be verified or discounted. Similarly, the complex spike evades a clear understanding when it comes to the cellular events underlying complex spike generation. What is known, however, is that complex spikes are associated with large dendritic calcium signals that are required for the induction of long-term depression (LTD) at the parallel fiber (PF)-PC synapse. PF-LTD is a form of long-term synaptic plasticity that has been suggested to underlie certain forms of cerebellar motor learning. In contrast to the PF input, the CF input has been considered invariant. Our recent discovery of LTD at the CF input shows that complex spikes are less static than previously assumed. In addition to depression of CF-evoked excitatory postsynaptic currents, long-lasting, selective reduction of slow complex spike components could be observed after brief CF tetanization. To understand the functional implications of CF-LTD, it is crucial to know the types of currents constituting the specific complex spike components. Here we review the "anatomy" of the complex spike as well as our observations of activity-dependent complex spike waveform modifications. In addition, we discuss which properties CF-LTD might add to the circuitry of the cerebellar cortex.