Piping systems are common in many architectures and designing such systems is often a complex task. Design automation of piping systems is therefore a universal research subject. Nonetheless, these piping systems are often still designed by hand as a result of their complexity. Consequently, costs associated with piping design are high, especially for large-scale architectures like ships and chemical plants. The goal of automatic pipe routing is to reduce the design time and associated costs of a piping system by automating the routing of these pipes. This survey provides an overview of the current state of automatic pipe routing literature to assist researchers and practitioners to further the study of automatic pipe routing. This is done by pinpointing and explaining the most important obstacles that stand in the way of making a full-scale automatic pipe routing method. The barriers that are analyzed are related to both model representation and optimization complexity. Finally, a synthesis table of research papers on automatic pipe routing is provided based on the handling of the aforementioned barriers and other general features of automatic pipe routing methodology. The survey concludes by discussing directions for further research.