In the language evolution literature there is a well-known paradox: human language appears very different from animal communication, but has to have come from somewhere evolutionarily. Since previously existing hominin species have all gone extinct, it’s nearly impossible to use them as a basis of comparison. Aside from fossilized bones, all that’s left to us are currently existing animal species. And at first blush their communication abilities – and those of other great apes – seem quite paltry relative to our own. Over the past 40 years, scholarly discussions of language evolution have become respectable again, after over a century of taboo, and so a fair amount of progress has been made in studying animal communication, both in the wild and in the laboratory. Here we compare it to human language on the basis of four characteristics. While animals exposed to human environments can be trained to understand basic symbolic representation, defined here as an arbitrary mapping between sign and referent, they never produce it on their own. Humans also have an extensive ability to refer to entities, properties and events well beyond the confines of the here and now, known as “displaced reference.” While isolated rudimentary examples of displaced reference can be found in both wild and trained animals, its occurrence is exceedingly rare. Human language also affords us the ability to combine meaningless elements – the sounds of spoken language and the manual features of sign language – into meaningful units, namely words or signs. These can in turn be combined into higher-level units – phrases and sentences – that retain and integrate the meanings of their individual parts in predictable ways. While such combinatorics were previously thought to be beyond the reach of other animals, recent research has revealed some surprising examples, especially in bird calls. There is also evidence that apes may be capable of simple combinations of this type in their gestural communication. In the end, a huge cleft remains between humans and other animals in their capacity for language, but we can identify isolated primitive building blocks of language-like behavior in their communicative repertoires.