Heterogeneous catalytic reactions and catalytic reactors are known to exhibit complex dynamic behavior and significant progress has been made, in the past two decades, in understanding this complexity using the tools of nonlinear dynamics and advanced experimental methods. This article presents an overview of complex dynamic behavior in heterogeneous catalysis and points out their intriguing nature along with practical implications. The issues discussed are the source of oscillatory behavior, classification of complex motions, transitions to chaotic solutions and spatiotemporal patterns in reactors of various geometries.