Diversifying return results is an important research topic in retrieval systems in order to satisfy both the various interests of customers and the equal market exposure of providers. There has been growing attention on diversity-aware research during recent years, accompanied by a proliferation of literature on methods to promote diversity in search and recommendation. However, diversity-aware studies in retrieval systems lack a systematic organization and are rather fragmented. In this survey, we are the first to propose a unified taxonomy for classifying the metrics and approaches of diversification in both search and recommendation, which are two of the most extensively researched fields of retrieval systems. We begin the survey with a brief discussion of why diversity is important in retrieval systems, followed by a summary of the various diversity concerns in search and recommendation, highlighting their relationship and differences. For the survey's main body, we present a unified taxonomy of diversification metrics and approaches in retrieval systems, from both the search and recommendation perspectives. In the later part of the survey, we discuss the open research questions of diversity-aware research in search and recommendation in an effort to inspire future innovations and encourage the implementation of diversity in real-world systems.