The study of spatial structures in heterogeneous reactors is a challenging academic topic, revealing patterns that differ from those known to exist in reaction-diffusion systems exposed to uniform conditions, as well as a practical problem that should affect design and operation procedures of commercial reactors like the catalytic convertor. Experimental observations and mathematical models of spatiotemporal patterns in high-pressure catalytic reactors are reviewed. Patterns in high-pressure reactors, in which thermal effects provide the positive feedback, as well as the long-range communication, usually emerge due to global interaction. Patterns are classified comprehensively by considering reactors of increasing degree of complexity: a wire or ribbon exposed to uniform conditions, a globally coupled catalyst in a mixed reactor or in a control loop, and a fixed bed in which interaction by convection occurs only in one direction. Catalytic wires are not expected to exhibit sustained patterns in the absence of global interaction. Global interactions by external control or gas-phase coupling are shown experimentally and analytically to induce a rich plethora of patterns. Complex motions were simulated to occur due to the interaction of convection, conduction and reaction in a fixed-bed; only a few of these patterns were experimentally observed. Directions for future research are suggested.