Spatiotemporal patterns reported to form in the cross sections of packed-bed reactors (PBRs) may pose severe safety hazard when present next to the reactor wall. Understanding what causes their formation and dynamic features is essential for the rational development of design and control strategies that circumvent their generation. We review the current knowledge and understanding about the formation of these transversal temperature patterns. Simulations and model analysis revealed that the formation of the hot spots and their dynamics are sensitive to the assumed kinetic and reactor models. Under practical conditions, stable symmetry-breaking bifurcation to nonuniform states, from stable, stationary, transversally uniform states cannot be predicted by common PBR models with a rate expression that depends only on the surface temperature and concentration of the limiting reactant. However, analysis and simulations reveal that transient nonuniform transversal temperatures may emerge in an upstream moving traveling front under practical conditions. Microkinetic oscillatory reactions predict the formation of a plethora of intricate spatiotemporal temperature patterns and temperature front motions that are sensitive to the reactor operating conditions and properties such as diameter and initial conditions. The predicted temperature patterns may be rather intricate as a result of conjugation of several modes. The nonlinear coupling between the states at different axial positions, that is, the interaction among the local temperature and concentrations at different cross-sections of the bed, may explain the intricate conjugation of several modes and modulation of the observed spatiotemporal patterns. While some simulations predicted spatiotemporal pattern evolution in PBRs, there is a need to understand which reaction mechanisms may lead to their formation. Most previous simulations and analysis utilized two-dimensional reactor models. However, hot zones are three-dimensional structures, often very small, and difficult to detect in large reactors. A 3-D simulation, although tedious, is necessary to provide full information about the size, shape and dynamic features of small hot zones. Moreover, common PBR models may have to be modified to account for the impact of local states such as flow distribution and nonuniform packing. Verification of the various model predictions requires in situ measurements of 3-D hot zones.