The Dutch have a remarkable history when it comes to height. From being one of the shortest European populations in the 19th Century, the Dutch grew some 20 cm and are currently the tallest population in the world. Wealth, hygiene, and diet are well-established contributors to this major increase in height. Some have suggested that natural selection may also contribute to the trend, but evidence is weak. Here, we investigate the potential role of natural selection in the increase in height through simulations. We first ask what if natural selection was solely responsible for the observed increase in height? If the increase in average height was fully due to natural selection on male height, then across six consecutive generations, men who were two standard deviation above average height would need to have eight times more children on average. If selection acted only through those who have the opportunity to reproduce, then reproduction would need to be restricted to the tallest third (37%) of the population in order to give rise to the stark increase in height over time. No linear relationship between height and child mortality is able to account for the increase over time. We then present simulations based on previously observed estimates of partnership, mortality, selection and heritability and show that natural selection had a negligible effect (estimates from 0.07 to 0.36 cm) on the increase in height in the period 1850 to 2000. Our simulations highlight the plasticity of height and how remarkable the trend in height is in evolutionary terms. Only by using a combination of methods and insights from different disciplines, including biology, demography, and history are we potentially able to address how much of the increase in height is due to natural selection versus other causes.