Nowadays Cloud computing permeates almost every domain in Information and Communications Technology (ICT) and, increasingly, most of the action is shifting from large, dominant players toward independent, heterogeneous, private/hybrid deployments, in line with an ever wider range of business models and stakeholders. The rapid growth in the numbers and diversity of small and medium Cloud providers is bringing new challenges in the as-a-Services space. Indeed, significant hurdles for smaller Cloud service providers in being competitive with the incumbent market leaders induce some innovative players to "federate" deployments in order to pool a larger, virtually limitless, set of resources across the federation, and stand to gain in terms of economies of scale and resource usage efficiency. Several are the challenges that need to be addressed in building and managing a federated environment, that may go under the "Security", "Interoperability", "Versatility", "Automatic Selection" and "Scalability" labels. The aim of this paper is to present a survey about the approaches and challenges belonging to the "Automatic Selection" category. This work provides a literature review of different approaches adopted in the "Automatic and Optimal Cloud Service Provider Selection", also covering "Federated and Multi-Cloud" environments
