Collaborative Information Retrieval (CIR) is a well-known setting in which explicit collaboration occurs among a group of users working together to solve a shared information need. This type of collaboration has been deemed as beneficial for complex or exploratory search tasks. With the multiplicity of factors impacting on the search effectiveness (e.g., col-laborators' interactions or the individual perception of the shared information need), CIR gives rise to several challenges in terms of collaboration support through algorithmic approaches. More particularly, CIR should allow to satisfy the shared information need by optimizing the collaboration within the search session over all collaborators while ensuring that both mutually beneficial goals are reached and that the cognitive cost of the collaboration does not impact the search effectiveness. In this survey, we propose an overview of CIR with a particular focus on the collaboration support through algorithmic approaches. The objective of this paper is (a) to organize previous empirical studies analyzing collaborative search with the goal to provide useful design implications for CIR models, (b) to give a picture of the CIR area by distinguishing two main categories of models using the collaboration mediation axis, and (c) to point out potential perspectives in the domain.