In recent years, the usage model of the Internet has changed, pushing researchers towards the design of the Information-Centric Networking (ICN) paradigm as a possible replacement of the existing architecture. Even though both Academia and Industry have investigated the feasibility and effectiveness of ICN, achieving the complete replacement of the Internet Protocol (IP) is a challenging task: (i) the process involves multiple parties, such as Internet Service Providers (ISPs), that need to coordinate among each other; (ii) it requires an indefinite amount of time to update hardware and software of network components; and (iii) it is a high risk goal that might introduce unexpected complications. Thus, the process of replacing the current Internet will inevitably lead towards a period of coexistence between the old and the new architectures. Given the urgency of the problem, this transition phase will happen very soon and people should address it in a smooth way.Some research groups have already addressed the coexistence by designing their own architectures, but none of those is the final solution to move towards the future Internet considering the unaltered state of the networking. To design such architecture, the research community needs now a comprehensive overview of the existing solutions that have so far addressed the coexistence. The purpose of this paper is to reach this goal by providing the first comprehensive survey and classification of the coexistence architectures according to their features (i.e., deployment approach, deployment scenarios, addressed coexistence requirements and additional architecture or technology used) and evaluation parameters (i.e., challenges emerging during the deployment and the runtime behaviour of an architecture). We believe that this paper will finally fill the gap required for moving towards the design of the final coexistence architecture.