This paper provides evidence that learning about demand is an important driver of firms' dynamics. We present a simple model with Bayesian learning in which firms are uncertain about their idiosyncratic demand parameter in each of the markets they serve, and update their beliefs as noisy information arrives in each period. The model predicts that firms update more their beliefs following a new demand shock, the younger they are. To test this learning mechanism, we make use of a specific feature of exporter-level data which contains both the values and the quantities sold by a given firm for the same product in different destination markets. This allows us to derive a methodology that identifies separately the demand shocks faced by the firms and their beliefs about future demand. We find strong support for our main prediction: The updating process appears especially strong in the first years after entry. However, the bulk of accumulated knowledge is lost during short periods of exit. Second, we consider implications of this prediction for firm growth rates and survival. Consistent with the learning model, we find that: (i) the absolute value of the mean growth rate for firms' beliefs decreases with age, as does the variance within cohorts; (ii) exit probability decreases with firms' beliefs and the demand shock the firm faces. Further, demand shocks trigger more exit in younger cohorts.