Invasion ecology has much advanced since its early beginnings. Nevertheless, explanation, prediction, and management of biological invasions remain difficult. We argue that progress in invasion research can be accelerated by, first, pointing out difficulties this field is currently facing and, second, looking for measures to overcome them. We see basic and applied research in invasion ecology confronted with difficulties arising from (A) societal issues, e.g., disparate perceptions of invasive species; (B) the peculiarity of the invasion process, e.g., its complexity and context dependency; and (C) the scientific methodology, e.g., imprecise hypotheses. To overcome these difficulties, we propose three key measures: (1) a checklist for definitions to encourage explicit definitions; (2) implementation of a hierarchy of hypotheses (HoH), where general hypotheses branch into specific and precisely testable hypotheses; and (3) platforms for improved communication. These measures may significantly increase conceptual clarity and enhance communication, thus advancing invasion ecology.