We review evidence for and against lateralization of manual control, communication, visual processing, and auditory processing in nonhuman primates. Compared to humans and some other vertebrate species, manual specialization in nonhuman primates is relatively weak. A right-bias in chimpanzees may exist, but is so weak that many studies using simple tasks fail to reveal it. Slightly stronger biases may exist in baboons and chimpanzees for communicative signals in the manual and facial domains. Several studies have found robust visual side biases that depend on the object being viewed, in primates including chimpanzees. Evidence for lateralization of auditory processing remains inconclusive. We conclude that the robust, species-wide lateralization that exists in humans is unusual, and perhaps unique among primates, and discuss several possible evolutionary explanations for this strong asymmetry. In particular, we consider the hypothesis that preexisting hemispheric asymmetry for perception and language processing drove the evolution of human handedness.