This chapter addresses a very complex problem that can be expressed in a very simple form: is it possible to automate surgery? We believe that, if a solution can ever be approached, it would lie in the intersection of robotics, automation, and cognition, since factors such as experience, knowledge, and intuition are as important as mechanism design and control algorithms in successful surgery. The feasibility of a solution to this problem was analyzed during the European project Intelligent Robotic Surgery (I-SUR), a project of the Seventh Framework Programme during the period 2011 to 2014. In this project, we developed general methods for cognitive surgical robots capable of combining sensing, dexterity, and cognitive capabilities to carry out autonomously simple surgical actions, such as puncturing and suturing. To narrow further the scope of this research, we addressed the well-known surgical area of kidney interventions, whose variability and uncertainty are limited, but still representative of general situations and requiring strong cognitive capabilities to ensure the correct execution of the surgery. We examined the reasoning aspects of these domains, the control capabilities needed to carry out these surgical actions, and we integrated them into a robotic test bed performing autonomous surgical actions on anatomically correct phantoms.