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Robots that physically interact with their surroundings, in order to accomplish some tasks or assist humans in their activities, require to exploit contact forces in a safe and proficient manner. Impedance control is considered as a prominent approach in robotics to avoid large impact forces while operating in unstructured environments. In such environments, the conditions under which the interaction occurs may significantly vary during the task execution. This demands robots to be endowed with on-line adaptation capabilities to cope with sudden and unexpected changes in the environment. In this context, variable impedance control arises as a powerful tool to modulate the robot's behavior in response to variations in its surroundings. In this survey, we present the state-of-the-art of approaches devoted to variable impedance control from control and learning perspectives (separately and jointly). Moreover, we propose a new taxonomy for mechanical impedance based on variability, learning, and control. The objective of this survey is to put together the concepts and efforts that have been done so far in this field, and to describe advantages and disadvantages of each approach. The survey concludes with open issues in the field and an envisioned framework that may potentially solve them.