Current research efforts to understand the relative invasibility of different plant communities have mostly ignored tropical forests. Only a few studies have treated invasive species in tropical forests, and recent worldwide analyses have not provided clear predictions concerning the relative invasibility of tropical forests. In this review, the extent to which exotic species have invaded tropical forests is summarized and four leading hypotheses to explain the apparently low frequency of invading plants in tropical forests are evaluated. In general, it is found that invasibility positively correlates with human disturbance, and that undisturbed tropical forests harbour few exotic species. To date, there is no evidence to attribute the low invasibility of undisturbed tropical forests to either their high species diversity or their high diversity of functional types. Instead, the low occurrence of exotic species in most tropical forests is most likely due to the fact that the great majority of exotic species that are transported to tropical countries lack specific life history traits, most importantly shade tolerance, necessary for successful invasion of undisturbed tropical forests. Unfortunately, this situation could change in the future with the expected increase in the plantation forestry of high-grade timber combined with common forestry practices that favour the cultivation of exotic species.