In recent years, digital endoscopy has established as key technology for medical screenings and minimally invasive surgery. Since then, various research communities with manifold backgrounds have picked up on the idea of processing and automatically analyzing the inherently available video signal that is produced by the endoscopic camera. Proposed works mainly include image processing techniques, pattern recognition, machine learning methods and Computer Vision algorithms. While most contributions deal with realtime assistance at procedure time, the post-procedural processing of recorded videos is still in its infancy. Many post-processing problems are based on typical Multimedia methods like indexing, retrieval, summarization and video interaction, but have only been sparsely addressed so far for this domain. The goals of this survey are (1) to introduce this research field to a broader audience in the Multimedia community to stimulate further research, (2) to describe domain-specific characteristics of endoscopic videos that need to be addressed in a pre-processing step, and (3) to systematically bring together the very diverse research results for the first time to provide a broader overview of related research that is currently not perceived as belonging together.