Entrepreneurship in most advanced economies is in decline. This comes as a surprise: many scholars have expected an upsurge in entrepreneurship. What are the reasons for the decline? In this paper I first document the extent of the decline in terms of entrepreneurial entry rates; the share of young and small firms; and in terms of labor market mobility and in innovativeness. I then critically discuss the explanations that have been offered in the literature, which variously ascribes the decline to either the slowing of population growth, and/or growing market concentration, zombie-firm congestion, slower diffusion of knowledge, and burdensome business regulations. While having merit, these explanations tend to take a supply-side view and moreover fail to explain why the decline in entrepreneurship is largely confined to economies with high levels of economic complexity. I argue that we need to consider the potential of negative scale effects and evolutionary pressures from rising complexity, as well as long-run changes in aggregate demand and energy costs. Whether the decline in entrepreneurship and the ossification of the economy is undesirable, is a point for debate, calling for more research and more attention to entrepreneurship in growth theories.