Edge computing is a (r)evolutionary extension of traditional cloud computing. It expands central cloud infrastructure with execution environments close to the users in terms of latency in order to enable a new generation of cloud applications. This paradigm shift has opened the door for telecommunications operators, mobile and fixed network vendors: they have joined the cloud ecosystem as essential stakeholders considerably influencing the future success of the technology. A key problem in edge computing is the optimal placement of computational units (virtual machines, containers, tasks or functions) of novel distributed applications. These components are deployed to a geographically distributed virtualized infrastructure and heterogeneous networking technologies are invoked to connect them while respecting quality requirements. The optimal hosting environment should be selected based on multiple criteria by novel scheduler algorithms which can cope with the new challenges of distributed cloud architecture where networking aspects cannot be ignored. The research community has dedicated significant efforts to this topic during recent years and a vast number of theoretical results have been published addressing different variants of the related mathematical problems. However, a comprehensive survey focusing on the technical and analytical aspects of the placement problem in various edge architectures is still missing. This survey provides a comprehensive summary and a structured taxonomy of the vast research on placement of computational entities in emerging edge infrastructures. Following the given taxonomy, the research papers are analyzed and categorized according to several dimensions, such as the capabilities of the underlying platforms, the structure of the supported services, the problem formulation, the applied mathematical methods, the objectives and constraints incorporated in the optimization problems, and the complexity of the proposed methods. We summarize the gained insights and important lessons learned, and finally, we reveal some important research gaps in the current literature.