We need to be sure of the importance of our Neolithic within the long-term story of human history: otherwise, we are in danger of becoming encapsulated within the minutiae of our expanding knowledge, and isolated from the wider world. Here is one way in which our Neolithic story can be shown to work as a critically important episode within the long-term of human history. There are three key features to the story of human evolution across more than two million years: gradually accelerating trends in cultural innovation and change, in the expansion of the range of cultural products, skills, and capacities, and in the growth of population density and the scale of human groups. When we focus down into the six millennia of the Epipalaeolithic-Neolithic transformation we can observe those three key features accelerating at an unprecedented rate. Leading evolutionary biologists, anthropologists, Palaeolithic archaeologists and philosophers are now explaining those long-term processes in terms of three cultural evolutionary mechanisms: gene-culture evolution, cultural niche construction, and cumulative culture. I conclude that our Epipalaeolithic-Neolithic transformation is similarly explicable in terms of contemporary cultural evolutionary theory, which enables us to tell the story of the great transformation in terms that are rapidly becoming universal.