Over the last few years, there has been a growing interest in communicative efficiency. It has been argued that language users act efficiently, saving effort for processing and articulation, and that language structure and use reflect this tendency. The emergence of new corpus data has brought to life numerous studies on efficient language use in the lexicon, in morphosyntax, and in discourse and phonology in different languages. In this introductory paper, we discuss communicative efficiency in human languages, focusing on evidence of efficient language use found in multilingual corpora. The evidence suggests that efficiency is a universal feature of human language. We provide an overview of different manifestations of efficiency on different levels of language structure, and we discuss the major questions and findings so far, some of which are addressed for the first time in the contributions in this special collection.