The amplification of the variance of order rates in multi-echelon systems, commonly known as ‘demand amplification’ or the ‘bullwhip effect’ is a widely discussed topic in the field of supply chain management. While a range of contributions have been made on how to counter this costly phenomenon, this paper shows why – after half a century of academic study – the problem still presents new challenges to the operations research community. In our historical review we have identified three distinct research domains that have addressed the problem – discrete time, the continuous time, and the frequency domain approaches – and discuss how these three approaches have interacted and influenced each other over time, consistently ‘pushing’ the frontiers of the bullwhip problem.