The importance of intraspecific trait variability for community dynamics and ecosystem functioning has been underappreciated. There are theoretical reasons for predicting that species that differ in intraspecific trait variability will also differ in their effects on ecosystem functioning, particularly in variable environments. We discuss whether species with greater trait variability are likely to exhibit greater temporal stability in their population dynamics, and under which conditions this might lead to stability in ecosystem functioning. Resolving this requires us to consider several questions. First, are species with high levels of variation for one trait equally variable in others? In particular, is variability in response and effects traits typically correlated? Second, what is the relative contribution of local adaptation and phenotypic plasticity to trait variability? If local adaptation dominates, then stability in function requires one of two conditions: (i) individuals of appropriate phenotypes present in the environment at high enough frequencies to allow for populations to respond rapidly to the changing environment, and (ii) high levels of dispersal and gene flow. While we currently lack sufficient information on the causes and distribution of variability in functional traits, filling in these key data gaps should increase our ability to predict how changing biodiversity will alter ecosystem functioning.