The Future Conversations workshop at CHIIR’21 looked to the future of search, recommendation, and information interaction to ask: where are the opportunities for conversational interactions? What do we need to do to get there? Furthermore, who stands to benefit? The workshop was hands-on and interactive. Rather than a series of technical talks, we solicited position statements on opportunities, problems, and solutions in conversational search in all modalities (written, spoken, or multimodal). This paper –co-authored by the organisers and participants of the workshop– summarises the submitted statements and the discussions we had during the two sessions of the workshop. Statements discussed during the workshop are available at https://bit.ly/FutureConversations2021Statements.