We describe here the ecological and evolutionary processes that modulate the effects of invasive species over time, and argue that such processes are so widespread and important that ecologists should adopt a long-term perspective on the effects of invasive species. These processes (including evolution, shifts in species composition, accumulation of materials and interactions with abiotic variables) can increase, decrease, or qualitatively change the impacts of an invader through time. However, most studies of the effects of invasive species have been brief and lack a temporal context; 40% of recent studies did not even state the amount of time that had passed since the invasion. Ecologists need theory and empirical data to enable prediction, understanding and management of the acute and chronic effects of species invasions.