Abstract: The first challenge for economic growth theory is to understand the transition from stagnation to growth at the time of the Industrial Revolution and in particular to identify the main factor(s) that triggered the take-off. Doing so also helps to understand why there are poor and rich countries today, and whether the poorest ones will ultimately catch-up. This chapter reviews the main theories of growth, including the Malthus model (useful to understand stagnation), the neo-classical model where technical progress is the engine of growth, the endogenous growth model where growth is self-sustained and policy is of particular importance for the long-run, and unified growth theory, providing the big picture and linking the growth take-off to the demographic transition.