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A wide range of factors drive the processes responsible for range dynamics following a successful invasion. These drive changes to the demographic and genetic qualities of the invasive species, potentially with long-term consequences. The invasion triangle encapsulates the complexity of the processes by organizing these factors into three major components: invader, site biotic characteristics, and environment. The invasion triangle is analogous to the disease triangle, which is foundational to the field of plant pathology. Yet, in the field of biological invasions, the model has been underutilised. By incorporating various factors attributed to invasions into the three components, the invasion triangle can be an invaluable tool in explaining both the success and collapse of invasive ranges. Here, we introduce a new interpretation of the invasion triangle that explicitly considers changes with time, and apply it to explain the changes in invasive species ranges. There is mounting evidence that invasiveness tends to reduce following successful initial invasion, particularly after an exponential increase in population. Drawing from the attributes of invaders and the observed changes in the ranges of invasive taxa, we explore different types of dynamics in the context of the invasion triangle. The new invasion triangle can form the basis for predicting change to invasive ranges, and should also prove useful in directing future research and management.