Explainable information retrieval is an emerging research area aiming to make transparent and trustworthy information retrieval systems. Given the increasing use of complex machine learning models in search systems, explainability is essential in building and auditing responsible information retrieval models. This survey fills a vital gap in the otherwise topically diverse literature of explainable information retrieval. It categorizes and discusses recent explainability methods developed for different application domains in information retrieval, providing a common framework and unifying perspectives. In addition, it reflects on the common concern of evaluating explanations and highlights open challenges and opportunities.