With the advent of Web search and the large amount of data published on the Web sphere, a tremendous amount of documents become strongly time-dependent. In this respect, the time dimension has been extensively exploited as a highly important relevance criterion to improve the retrieval effectiveness of document ranking models. Thus, a compelling research interest is going on the temporal information retrieval realm, which gives rise to several temporal search applications. In this article, we intend to provide a scrutinizing overview of time-aware information retrieval models. We specifically put the focus on the use of timeliness and its impact on the global value of relevance as well as on the retrieval effectiveness. First, we attempt to motivate the importance of temporal signals, whenever combined with other relevance features, in accounting for document relevance. Then, we review the relevant studies standing at the crossroads of both information retrieval and time according to three common information retrieval aspects: the query level, the document content level and the document ranking model level. We organize the related temporal-based approaches around specific information retrieval tasks and regarding the task at hand, we emphasize the importance of results presentation and particularly timelines to the end user. We also report a set of relevant research trends and avenues that can be explored in the future.