Although our understanding of the cellular properties of mammalian neurons is increasing rapidly, the computational function of their elaborate dendritic trees is still mysterious. In recent years, experiments have shown that, in pyramidal cells, individual dendritic compartments sustain local excitation spikes.. These dendrites also support Hebbian synaptic plasticity, which depends on the precise temporal relationship between pre- and postsynaptic spikes. In this review we discuss what we consider to be a problem with Hebbian (i.e., spike-timing-dependent) plasticity. We argue that most of the spikes that occur in dendrites are not back-propagating action potentials but but local spikes, and that Hebbian plasticity caused by local spikes can undermine the functional integrity of the geometrically complex dendritic tree. We propose that the inverted Hebbian plasticity of synapses involved in local spikes, and/or local dendritic homeostatic plasticity, could prevent an unbalanced distribution of synaptic weights on the dendritic tree.