Catalysis is at the core of almost every established and emerging chemical process and also plays a central role in the quest for novel technologies for the sustainable production and conversion of energy. Particularly since the early 2000s, a great surge of interest exists in the design and application of micro- and nanometer-sized materials with hollow interiors as solid catalysts. This review provides an updated and critical survey of the ever-expanding material architectures and applications of hollow structures in all branches of catalysis, including bio-, electro-, and photocatalysis. First, the main synthesis strategies toward hollow materials are succinctly summarized, with emphasis on the (regioselective) incorporation of various types of catalytic functionalities within their different subunits. The principles underlying the scientific and technological interest in hollow materials as solid catalysts, or catalyst carriers, are then comprehensively reviewed. Aspects covered include the stabilization of catalysts by encapsulation, the introduction of molecular sieving or stimuli-responsive "auxiliary" functionalities, as well as the single-particle, spatial compartmentalization of various catalytic functions to create multifunctional (bio)catalysts. Examples are also given on the applications which hollow structures find in the emerging fields of electro- and photocatalysis, particularly in the context of the sustainable production of chemical energy carriers. Finally, a critical perspective is provided on the plausible evolution lines for this thriving scientific field, as well as the main practical challenges relevant to the reproducible and scalable synthesis and utilization of hollow micro- and nanostructures as solid catalysts.