Since language is basically audio-vocal communications in humans, the vocal communication in nonhuman primates has been discussed with the questions for evolutionary origins of languages. Many studies have accumulated many empirical evidences showing similarities as well as gaps between human languages and nonhuman primate vocal communications. Here I briefly reviewed the research history of the studies for vocal communications in nonhuman primates, which have been mainly directed to search for origins of human languages. Generally, there are two major approaches for primate origins of human languages; 1) studies of vocal communication in nonhuman primates would contribute to understanding the origins of languages, or 2) it would be completely different forms of language and never contribute to its understanding. The first brief is arisen from the ethological studies for alarm calls, using playback experiments in wild animals. Those studies have showed semantic rules in their communications, which had been believed as a unique component of human language. However, their anatomical and physiological foundations never support vocal plasticity and learning ability in nonhuman primates, which are essential properties in human languages. Those usually lead to the second brief. It would be difficult to solve this critical discrepancy, because both ideas likely discuss the origins of languages with wrong views of unidirectional way in language evolution, i.e., the way from nonhuman primates to humans. Human languages is not the most complex fashion of vocal communications in primate lineages, but vocal communications in other primate species are also complex and unique styles. Now we need more careful attentions to communication uniqueness of various kinds of primate species as well as language uniquness.