Tufted capuchin monkeys (Cebus apella), a species of New World primates, are known to be adept at various complex tool use both in the laboratory and in the wild. With their manual dexterity, they work as a helper for quadriplegic people. Social intelligence hypothesis, which places social intelligence as a major factor to advance complex information processing capability, predicts advanced social intelligence in this species with highly developed physical intelligence. In this paper, I describe a series of studies on social intelligence of this species in our comparative cognition laboratory at Kyoto University. As a competitive aspect of social intelligence, we analyzed spontaneous deceptive behavior between the monkeys. Two monkeys, dominant and subordinate, faced each other in the transparent boxes and two food cups were placed between them. When the subordinate monkey opened the baited cup, the dominant opponent was able to usurp the food. Some of the subordinates started to open the empty cup first: a behavior that could be interpreted as a deceptive act. As a cooperative aspect, we showed that two monkeys cooperated by dividing a sequence of behavior necessary to obtain rewards. This behavior continued even when only one of the participants received a reward if their roles were switched every trial; a reciprocal altruism was shown. To examine whether such complicated social behaviors reflect processes of mentalizing, we asked whether capuchin monkeys have cognitive components underlying them. We found that the monkeys are capable of recognizing attentional states of humans, inferring consequences of other's behavior, recognizing other's knowledge status, inferring the cause of other's emotional expression, and recognizing other's welfare. Thus these primitive aspects of mentalizing are clearly shared in species that is much more distant from humans than apes.