Invasive species have transformed local, regional and global biotas; however, few generalities about the mechanisms driving impacts of invaders have emerged. To explain variation in impacts among studies, we propose a broad framework that separates drivers of impacts into universal and unique attributes of the invasive species and the invaded habitat. Universal attributes are relevant to all invasions whereas unique attributes are distinct to a specific invasion. For example, impacts associated with the abundance of any invader or the properties of a specific invader (e.g., a rare toxin) represent a universal and unique impact attribute. Through meta-analyses of aquatic field experiments, we demonstrate the utility of our framework, documenting that both the abundance and the taxonomic identity of the invader significantly influence invasion outcomes for marine and freshwater plant and animal invaders. Our review also highlights that many more experiments are needed to test for universal attributes, such as priority effects, age and size, and how the attributes of the invaded habitat further modify invasion impacts. We hope that our framework will stimulate experimental invasion ecology and begin to reconcile the idiosyncrasies that currently impede the development of a unified framework for invasion impacts.