In free-space optics, invisibility cloaking is fundamentally limited by relativity, making passive broadband, macroscopic cloaks impossible. This thesis explores invisibility cloaking beyond ballistic optics. In the regimes of heat conduction and light diffusion, the relativity problem vanishes due to inherently slower energy transport. Macroscopic cloaks for transient heat flow and static diffusive light transport are designed, realized and experimentally characterized