Shared control is an increasingly popular approach to facilitate control and communication between humans and intelligent machines. However, there is little consensus in guidelines for design and evaluation of shared control, or even in a definition of what constitutes shared control. This lack of consensus complicates cross fertilization of shared control research between different application domains. This paper provides a definition for shared control in context with previous definitions, and a set of general axioms for design and evaluation of shared control solutions. The utility of the definition and axioms are demonstrated by applying them to four application domains: automotive, robot-assisted surgery, brain-machine interfaces, and learning. Literature is discussed for each of these four domains in light of the proposed definition and axioms. Finally, to facilitate design choices for other applications, we propose a hierarchical framework for shared control that links the shared control literature with traded control, co-operative control, and other human-automation interaction methods. Future work should reveal the generalizability and utility of the proposed shared control framework in designing useful, safe, and comfortable interaction between humans and intelligent machines.