Current understanding and open questions concerning formation and motion of temperature fronts and patterns in packed-bed reactors and on single catalytic pellets are reviewed. For the single-reaction case, it is possible to readily predict the maximal temperature of fronts formed in packed-bed reactors following sudden changes in the feed conditions (wrong-way behavior) or during reverse-flow operation. There is a need to extend these relations for systems involving multireactions and reversible changes in the pellet state. Complex temperature patterns may be generated on catalytic surfaces by global interaction and surface nonuniformities. Simulations predict that even more intricate patterns may evolve in packed-bed reactors. It is still unresolved which of these complex patterns exist in commercial reactors, what is their impact, and which control policies can stabilize beneficial temperature patterns. The predictions of several important dynamic features, such as hot-spot formation, await further analysis of models which account also for the momentum transport and changes in the physical properties of the fluid in the reactor.