While the impact of exchange rate changes on economic growth has long been an issue of key importance in international macroeconomics, it has received renewed attention in recent years, owing to weaker growth rates and the debate on "currency wars". However, in spite of its prevalence in the policy debate, the connection between real exchange rates and growth remains an unsettled question in the academic literature. We fill this gap by providing an empirical assessment based on a broad sample of emerging and advanced economies. We assess the impact of appreciations, productivity booms and capital inflows surges using a propensity-score matching approach to address causality issues. We show that appreciations associated with higher productivity have a larger impact on growth than appreciations associated with capital inflows. Furthermore, the appreciation per se tends to have a negative impact on growth. We provide a simple theoretical model that delivers the contrasted growth-appreciation pattern depending on the underlying shock. The model also implies adverse effects of shocks to international capital flows, so concerns about an appreciation are not inconsistent with concerns about a depreciation. The presence of an externality through firms' destruction leads to inefficient allocations. Nonetheless, addressing them does not require a dampening of exchange rate movements.