In the last five years, deep learning has attracted great interest in computer-assisted systems for Minimally Invasive Surgery. The straightforward accessibility to images in surgical interventions makes deep neural networks enormously powerful for solving classification problems in complex surgical scenarios. The objective of this work is to provide readers a survey on deep learning models applied to minimally invasive surgery, identifying the different architectures used depending on the application, the results achieved until now, and the publicly available surgical datasets that can be used for validating new studies. A total of 85 publications have been extracted from manual research from four databases (IEEE Xplorer, Springer Link, Science Direct, and ACM Digital Library). After analyzing all these studies, they have been classified into four applications: surgical image analysis, surgical task analysis, surgical skill assessment, and automation of surgical tasks. This work provides a technical description of these works and a comparison among them. Finally, promising research directions to advance in this field are identified.