Fungal invasions are increasingly recognized as a significant component of global changes, threatening ecosystem health and damaging food production. Invasive fungi also provide excellent models to evaluate the generality of results based on other eukaryotes. We first consider here the reasons why fungal invasions have long been overlooked: they tend to be inconspicuous, and inappropriate methods have been used for species recognition. We then review the information available on the patterns and mechanisms of fungal invasions. We examine the biological features underlying invasion success of certain fungal species. We review population structure analyses, revealing native source populations and strengths of bottlenecks. We highlight the documented ecological and evolutionary changes in invaded regions, including adaptation to temperature, increased virulence, hybridization, shifts to clonality and association with novel hosts. We discuss how the huge census size of most fungi allows adaptation even in bottlenecked, clonal invaders. We also present new analyses of the invasion of the anther-smut pathogen on white campion in North America, as a case study illustrating how an accurate knowledge of species limits and phylogeography of fungal populations can be used to decipher the origin of invasions. This case study shows that successful invasions can occur even when life history traits are particularly unfavourable to long-distance dispersal and even with a strong bottleneck. We conclude that fungal invasions are valuable models to contribute to our view of biological invasions, in particular by providing insights into the traits as well as ecological and evolutionary processes allowing successful introductions.