The phyllosphere is a wide and complex ecosystem that provides a key support for microbial diversity. Fungal communities inhabiting the leaf are functionally variable and play important roles on plant performance. Factors conditioning the arrival and colonization of fungal communities will determine the phyllosphere fungal composition. Plant identity, leaf functional traits and host plant phylogeny have been shown to be regulators of the microbial colonization of the leaves, and can be considered as biotic filters determining the assembly of phyllosphere fungal communities. By high‐throughput sequencing we analysed the phyllosphere fungal communities from 38 Mediterranean woody plant species in two forests of south‐eastern Iberian Peninsula. We analysed the effect of plant species and site on fungal community composition. We also tested the effect of leaf functional traits and plant phylogeny on plant species differences in their fungal communities, and on the structure of the plant–fungus interaction network. Plant species account for a larger proportion than site in the variability of the composition of phyllosphere fungal communities. Leaf traits and host phylogeny influence the arrival and colonization of phyllosphere fungal communities across plant species. Plants with pubescent leaves and phylogenetically closer harbour more similar communities of decomposers, pathogens and epiphytes. Leaf habit (i.e. evergreen versus deciduous) also influences the community composition of decomposer and epiphytic fungi. Leaf carbon, leaf water content and leaf mass per area affect differentially each functional guild. Plant–fungus interaction networks present a modular structure in which plants belonging to the same module share more fungal species and are phylogenetically closer. We provide evidence that even though phyllosphere fungal communities are complex ecosystems, fungi with contrasting relationships with the plant (decomposers, epiphytes and pathogens) respond similarly to a common subset of leaf traits that impose physical limitations to the assembly of phyllosphere fungal communities.