Today’s world is full of instances of hyper-exponential growth (HEG). Clear examples of HEG have been identified, including the increase of the human population, the world economy and many aspects of technology. While hyper-exponential growth appears less often in natural sciences than exponential growth, it is especially important to understand of much that is happening today. Models of HEG have been developed to understand biological phenomena such as cancer growth and the dynamics of epidemics such as SARS-CoV-2. In this talk I will develop an epidemic model with evolution of transmission rates to show how HEG emerges naturally in a complex biological system. Solving the equations of growth, I show how many of the phenomena associated with HEG, such as asymptotic increase in finite time, can be understood. Finally, I apply these insights to the wider issues of importance, such as what is the nature of the collapse of hyper-exponential growth if it happens.