I'll introduce finite dynamical complexity, a notion of 'tractability' for topological dynamical systems. It generalizes the finite decomposition complexity of Guentner, Tessera and Yu: for example, a group has finite decomposition complexity if and only if its canonical action on its Stone-Čech compactification has finite dynamical complexity. I'll give some examples, and discuss applications to computing K-theory.

This is joint work with Erik Guentner and Guoliang Yu.