A major problem of neurobiology concerns the failure of injured mammalian spinal cord to repair itself. This review summarizes work done on two preparations in which regeneration can occur: the central nervous system of an invertebrate, the leech, and the spinal cord of an immature mammal, the opossum. The aim is to understand cellular and molecular mechanisms that promote and prevent regeneration. In the leech, an individual axon regrows successfully to re-establish connections with its synaptic target, while avoiding other neurons. Functions that were lost are thereby restored. Moreover, pairs of identified neurons become re-connected with appropriate synapses in culture. It has been shown that microglial cells and nitric oxide play key roles in leech CNS regeneration. In the opossum, the neonatal brain and spinal cord are so tiny that they survive well in culture. Fibres grow across spinal cord lesions in neonatal animals and in vitro, but axon regeneration stops abruptly between postnatal days 9 and 12. A comprehensive search has been made in spinal cords that can and cannot regenerate to identify genes and establish their locations. At 9 days, growth-promoting genes, their receptors and key transcription molecules are up-regulated. By contrast at 12 days, growth-inhibitory molecules associated with myelin are prominent. The complete sequence of the opossum genome and new methods for transfecting genes offer ways to determine which molecules promote and which inhibit spinal cord regeneration. These results lead to questions about how basic research on mechanisms of regeneration could be 'translated' into effective therapies for patients with spinal cord injuries.