The empirical finding that exporting firms are more productive on average than non-exporters has provoked a large theoretical literature based on models such as Melitz (2003), where more productive firms are more likely to overcome costs associated with trade. This paper investigates how closely the productivity heterogeneity framework fits the data from a firm-level survey that includes information on export destinations and firm characteristics such as productivity. We find a high degree of unpredictable idiosyncratic participation in export markets by firms and a relatively weak positive correlation between the extent of a firm's export market participation and its export sales. We find that a small number of standard gravity variables provide a close fit to the country-level determinants of trade but that greater variation results in more difficulty in explaining firm-specific factors driving exporting behaviour. We also illustrate some elements of the dynamics over time in firm exporting patterns by destination. We show that lagged exporting activity has a significant effect on a firm's current exporting profile.