Important advances in experimental methods have made it possible to measure the electrical events in dendrites directly and to record optically from dendritic spines. These new techniques allow us to focus on the input region of the neuron and highlight the excitable properties of the dendritic membrane. Interestingly, some of the recent experimental findings were anticipated by earlier theoretical research, for example, the observation that some spines possess excitable channels that might generate local all-or-none events. Computer models were used previously to explore the conditions for initiating an action potential at the dendritic tree, in particular, at the spine head, and for active propagation between excitable spines and excitable dendritic arbors. The consequences for synaptic amplification, for the extent of active spread in the tree and for non-linear discriminations between different patterns of synaptic inputs were also considered. Here we review the biophysical insights gained from the theory and demonstrate how these elucidate the recent experimental results.