The global decline of biodiversity caused by human domination of ecosystems worldwide is supposed to alter important process rates and state variables in these ecosystems. However, there is considerable debate on the prevalence and importance of biodiversity effects on ecosystem function (BDEF). Here, we argue that much of the debate stems from two major shortcomings. First, most studies do not directly link the traits leading to increased or decreased function to the traits needed for species coexistence and dominance. We argue that implementing a trait-based approach and broadening the perception of diversity to include trait dissimilarity or trait divergence will result in more realistic predictions on the consequences of altered biodiversity. Second, the empirical and theoretical studies do not reflect the complexity of natural ecosystems, which makes it difficult to transfer the results to natural situations of species loss. We review how different aspects of complexity (trophic structure, multifunctionality, spatial or temporal heterogeneity, and spatial population dynamics) alter our perception of BDEF. We propose future research avenues concisely testing whether acknowledging this complexity will strengthen the observed biodiversity effects. Finally, we propose that a major future task is to disentangle biodiversity effects on ecosystem function from direct changes in function due to human alterations of abiotic constraints.