Living languages continuously evolve to reflect the cultural changes of human societies. This evolution manifests through neologisms (new words) or the semantic change of existing words (new meanings for existing words). Understanding the meaning of words is vital for interpreting texts from different cultures (regionalisms or slang), domains (e.g., technical terms), or time periods. In computer science, this phenomenon is relevant to computational linguistics tasks such as machine translation, information retrieval, and question answering. Semantic change can impact the performance of these applications, making it important to understand and characterize these changes formally. This problem has recently attracted significant attention from the computational linguistics community. Several approaches can detect semantic changes with good precision, but more effort is needed to characterize how word meanings change and to determine how to mitigate the impact of this phenomenon. This survey provides a comprehensive overview of existing approaches to the characterization of semantic change. We also formally define three classes of characterization: change in dimension (whether a word’s meaning becomes broader or narrower), change in orientation (whether a word acquires a more pejorative or ameliorative sense), and change in relation (whether a word is used in a new figurative context, such as a metaphor or metonymy). We demonstrate the applicability of this formalism on existing corpora, summarize the key aspects of selected publications, and discuss current needs and trends in research on semantic change characterization.