Undoubtedly, hydrogen (H2) is a clean feedstock and energy carrier whose sustainable production should be anticipated. The pyrolysis of biomass or waste plastics and the subsequent reforming over base (transition) or noble metals supported catalysts allows reaching elevated H2 yields. However, the catalyst used in the reforming step undergoes a rapid and severe deactivation by means of a series of physicochemical phenomena, including metal sintering, metallic phase oxidation, thermal degradation of the support and, more notoriously, coke deposition. This review deals with the currently existing alternatives at the catalyst and reactor level to cope with catalyst deactivation and increase process stability, and then delves with the fundamental phenomena occurring during this catalyst deactivation. An emphasis is placed on coke deposition and its influence on deactivation, which depends on its location, chemical nature, morphology, precursors or formation mechanism, among others. We also discuss the challenges for increasing the value of the carbon materials formed and therefore, enhance process viability.