Tree hollows support a specialised species-rich fauna. We review the habitat requirements of saproxylic (= deadwood dependent) invertebrates which occupy tree hollows. We focus on studies quantifying relationships between species occurrence patterns and characteristics of tree hollows, hollow trees, and the surrounding landscape. We also explore the processes influencing species occurrence patterns by reviewing studies on the spatio-temporal dynamics of populations, including their dispersal and genetic structure. Our literature search in the database Scopus identified 52 relevant publications, all of which were studies from Europe. The dominant taxonomic group studied was beetles. Invertebrates in hollow trees were often more likely to be recorded in trees with characteristics reflecting a large amount of resources or a stable and warm microclimate, such as a large diameter, large amounts of wood mould (= loose material accumulated in the hollows mainly consisting of decaying wood), a high level of sun exposure, and with entrance holes that are large and either at a low or high height, and in dry hollows, with entrances not directed upwards. A stable microclimate is probably a key factor why some species of saproxylic invertebrates are confined to tree hollows. Other factors that are different in comparison to downed dead wood is the fact that hollows at a given height from the ground provide shelter from ground-living predators, that hollows persist for longer, and that the content of nutrients might be enhanced by the accumulation of dead leaves, insect frass, and remains from dead insects. Several studies have identified a positive relationship between species occupancy per tree and the amount of habitat in the surrounding landscape, with a variation in the spatial scale at which characteristics of the surrounding landscape had the strongest effect over spatial scales from 200 to 3000 m. We found empirical support for the extinction threshold hypothesis, which predicts that the frequency of species presence per tree is greater if a certain number of trees are aggregated into a few large clusters of hollow trees rather than distributed among many small clusters. Observed thresholds in species occurrence patterns can be explained by colonisation-extinction dynamics, with species occupancy per tree influenced by variation in rates of immigration. Consistent with this assumption, field studies suggest that dispersal rate and range can be low for invertebrates occupying tree hollows, although higher in a warmer climate. For one species in which population dynamics has been studied over 25 years (Osmoderma eremita), the observed population dynamics have characteristics of a "habitat-tracking metapopulation", as local extinctions from trees occur possibly because those trees become unsuitable as well as due to stochastic processes in small populations. The persistence of invertebrate fauna confined to tree hollows may be improved by prolonging the standing life of existing hollow trees. It is also important to recruit new generations of hollow trees, preferably close to existing larger groups of hollow trees. Thus, the spatio-temporal dynamics of hollow trees is crucial for the invertebrate fauna that rely upon them.