Mirror neurons for manipulation fire both when the animal manipulates an object in a specific way and when it sees another animal (or the experimenter) perform an action that is more or less similar. Such neurons were originally found in macaque monkeys, in the ventral premotor cortex, area F5 and later also in the inferior parietal lobule. Recent neuroimaging data indicate that the adult human brain is endowed with a "mirror neuron system," putatively containing mirror neurons and other neurons, for matching the observation and execution of actions. Mirror neurons may serve action recognition in monkeys as well as humans, whereas their putative role in imitation and language may be realized in human but not in monkey. This article shows the important role of computational models in providing sufficient and causal explanations for the observed phenomena involving mirror systems and the learning processes which form them, and underlines the need for additional circuitry to lift up the monkey mirror neuron circuit to sustain the posited cognitive functions attributed to the human mirror neuron system.