GKM theory is a well-known description of torus-equivariant cohomology at the interface of symplectic geometry and algebraic topology developed by Goresky, Kottwitz, and MacPherson using ideas from many other mathematicians. We describe how the GKM presentation of the equivariant cohomology ring is one example of a more general object called an algebraic spline that is essentially dual to the classical splines of analysis and applied mathematics. We also show ways that this more general perspective can streamline arguments, invite more and different techniques, and pose new questions.