Despite the growing importance and use of mediation as a form of conflict resolution, and the significant importance that communication and interaction have in the process, national and international mediation manuals, which are mainly theoretical and/or focused on legal commentaries, have little to say about real encounters between mediators and disputants, that is, how mediation-in-interaction works in fact. Based on the contributions from Conversation Analysis, this empirical qualitative research seeks to understand how the institution of mediation is co-constructed among participants, as well as to describe how different verbal and non-verbal linguistic resources are mobilized by mediators in the construction of interactional practices aligned with their institutional mandate. More precisely, this research zooms in on the (re)formulation practices performed by mediators in interactional sequences in which at least one of the parties complains, accuses or blames the other, in order to: (i) describe mediators (re)formulations of what one party said to/about the other; (ii) describe and analyze the actions and outcomes (re)formulations are designed to produce; (iii) examine the role of (re)formulations in mediation and their relations to the mediator s institutional tasks. For this purpose, a corpus was generated consisting of 26 hours of audio-recorded extrajudicial family mediation sessions that took place in a Legal Practice Center of a university in the state of Rio de Janeiro. The analysis of the (re)formulation practices shows us how different institutional goals are made relevant and can be achieved by mediators from the transformations of previous turns at talk and alternative interpretation offers. Among them are the mitigation and/or neutralization of the escalation of the conflict between the parties and the transformation of relational and subjective issued into mediatable topics. Most notably, we observed the role of (re)formulations in (re)directing the parties to a position in which they can cooperate, or at least find a set of common elements on which they can build in subsequent discussions in mediation, enabling the progression of mediation sessions and providing opportunities for future changes in the relationship and interaction between the parties. In this sense, this study contributes, in theoretical terms, to the study of the phenomenon of (re)formulation and, in applied terms, to the training of mediators.