Global food security faces great challenges due to growing population and income, as well as shifting dietary preferences. Despite advancements in agricultural practices and technologies that have increased crop production, the recent food crisis has highlighted the importance of understanding multiple factors (such as climate change) that can exacerbate food insecurity. As a result, in order to understand the opportunities and challenges to meeting rising food demand and achieving a more stable food supply, it is critical to characterize the spatiotemporal patterns of crop yield by investigating long-term crop yield trends, crop yield shocks, and international crop trade networks, as well as the drivers (i.e., socioeconomic and ecological) of crop production and supply. In the context of global food systems and food security, this dissertation, divided into three core chapters, seeks to systematically investigate one critical dimension of food security (i.e., stability) by analyzing the production and supply of crop commodities with statistical and machine learning approaches. Crop yield stagnation in several global regions poses a significant challenge to meeting 2050 food demand targets, necessitating an examination of historical long-term trends of crop yields and their drivers. Such an assessment is also important to project the amount of nitrogen (N) required to meet the 2050 targets. To accomplish this goal, we used a massive global dataset of N budget at the national scale and quantified the long-term yield response relationships with yield response functions for each of the eleven major crop types (Chapter 2). These relationships were then used to predict global N inputs in cropland in 2050 by scenario designs that took into account various technology and management practices (TMP) levels. The findings highlighted the importance of TMP in reducing the load of excess N in cropland while meeting rising food demand. In addition to investigating the long-term trends in crop yields, assessing sudden reductions in crop yields is equally important to sustaining and meeting food demand (Chapter 3). We quantified the sharp drops in wheat yield (i.e., shocks) and their drivers (i.e., ecological and socioeconomic) using quantile regression techniques. This analysis revealed the pressing issue of large crop yield reductions due to extreme weather stress. It also demonstrates that technological advances (per capita gross domestic product (GDP)) and resource inputs (e.g., N fertilization) have been focusing on achieving higher crop yields rather than mitigating yield shocks. Disruptions in the availability of crops, whether caused by shocks or stagnation, can be balanced through international trade by exchanging commodities from surplus to deficit regions; hence, international trade plays an important role in stabilizing food supply (Chapter 4). However, the risk associated with higher levels of extreme weather stress and synchronous crop yield fluctuations among countries significantly alters international trade links, jeopardizing food system resilience. We characterized the relationships between these two factors and international wheat trade partnerships using a flexible framework of an exponential random graph model (ERGM) and random forest. According to the analysis, the resilience of international wheat trade could be improved if countries can adjust trade portfolios by considering the level of extreme weather stress and concurrent yield variations with their trading partners. Overall, the dissertation expands on previous research by comprehending the role of ecological and socioeconomic drivers on crop production and supply, as well as proposing policies to mitigate the negative impact of these drivers on key aspects of global crop supply stability.