This thesis consists of three independent chapters. The first co-authored chapter studies the determinants of preference utilization. We show that it is increasing in the share of competitors' exports that are eligible to preferential treatment and that reciprocal preferences display higher utilization rates compared to non reciprocal ones. In addition, we find that an increase in domestic value added reduces both underutilization and its sensitivity to trade policy changes. The second co-authored chapter builds a partial equilibrium model to quantify to what extent Least Developed Countries (LDCs) will be affected by graduation from the LDC status. We project that graduation will have a negative impact on trade, but such adverse effects will be mitigated by the current underutilization of LDC duty schemes. On the other hand, we simulate a scenario in which all Lest Developed Countries simultaneously switch to a full preference utilization regime and quantify the potential benefits of removing the obstacles to the use of preferences. The third chapter, which is single-authored, exploits Italian customs data to study the impact of Covid-19 on firm-level trade. I show that the pandemic in foreign countries had a negative impact on imports and exports, especially during the first wave. I find that less intensively traded varieties had a higher probability of being dropped in the aftermath of the Covid-19 crisis, and that the varieties that were displaced in 2020 had a higher probability of not being traded one year later, which preliminarily suggests that the trade impact of Covid-19 might be persistent.