What do animal signals mean? This is a central question in studies on animal communication. Research into the semantics of animal signals began in 1980, with evidence that alarm calls of a non-human primate designated predators as external referents. These studies have challenged the historical assumption that such referential signaling is a unique feature of human language and produced a paradigm shift in animal communication research. Over the past two decades, an increasing number of field studies have revealed similar complexity in anti-predator communication of birds. The acoustic structures of avian alarm calls show a high degree of variation in pitch, duration, shape, and repetition rate. In addition to such distinct and graded variations, several birds combine discrete types of notes or calls into higher complex sequences. These variations in alarm calls are typically associated with the predator’s attributes, such as predator type and distance, and receivers respond to them with appropriate anti-predator behaviors. Although alarm calls of several bird species, as well as those of monkeys, appear to denote predator attributes, almost nothing is known about the cognitive processes that underlie the production and perception of these signals. In this review, I explore the existing evidence for referential signaling in birds and highlight the importance of the cognitive approach to animal communication research. I hope this review will promote further investigations of alarm-calling behavior in birds and will help enhance our understanding of the ecology and evolution of semantic communication.