The tremendously unbalanced distribution of species richness across clades in the tree of life is often interpreted as the result of variation in the rates of diversification, which may themselves respond to trait evolution. Even though this is likely a widespread pattern, not all diverse groups of organisms exhibit heterogeneity in their dynamics of diversification. Testing and characterizing the processes driving the evolution of clades with steady rates of diversification over long periods of time are of importance in order to have a full understanding of the buildup of biodiversity through time.We studied the macroevolutionary history of the species rich tree fern family Cyatheaceae and inferred a time calibrated phylogeny of the family including extinct and extant species using the recently developed fossilized birth-death method. We tested whether the high diversity of Cyatheaceae is the result of episodes of rapid diversification associated with phenotypic and ecological differentiation or driven by stable but low rates of diversification. We compared the rates of diversification across clades and modelled the evolution of body size and climatic preferences and tested for trait-dependent diversification.This ancient group diversified at a low and constant rate during its long evolutionary history. Morphological and climatic niche evolution were found to be overall highly conserved, although we detected several shifts in the rates of evolution of climatic preferences, linked to changes in elevation. The diversification of the family occurred gradually, within limited phenotypic and ecological boundaries, and yet resulted in a remarkable species richness.Our study indicates that Cyatheaceae is a diverse clade which slowly accumulated morphological, ecological, and taxonomic diversity over a long evolutionary period and provides a compelling example of tropics as a museum of biodiversity.