Endoscopic procedures form part of routine clinical practice for minimally invasive examinations and interventions. While they are beneficial for the patient, reducing surgical trauma and making convalescence times shorter, they make orientation and manipulation more challenging for the physician, due to the limited field of view through the endoscope. However, this drawback can be reduced by means of medical image processing and computer vision, using image stitching and surface reconstruction methods to expand the field of view. This paper provides a comprehensive overview of the current state of the art in endoscopic image stitching and surface reconstruction. The literature in the relevant fields of application and algorithmic approaches is surveyed. The technological maturity of the methods and current challenges and trends are analyzed.