Rising inequality is a significant challenge of our time, as more advantaged regions and populations are better equipped to benefit from urbanization, globalization, and technological advancements, while disadvantaged areas and populations bear the brunt of economic and environmental disruptions due to their limited adaptive capacities. Spatial disparities lead to adverse economic, social, and political consequences. This dissertation examines spatial inequalities in African countries, focusing on child nutrition, poverty, and climate vulnerability. The three papers investigate the impact of urbanization on child nutrition, the role of spatial heterogeneity in poverty mapping, and the interaction between climate risks and vulnerabilities. Collectively, they contribute to the discourse on inclusive development and resilience building in Africa. The first paper investigates the impact of urbanization on child nutritional outcomes across 18 African countries over two decades. Using a quasi-natural experiment with difference-in-differences and matching techniques, it finds that children born in settlements that have transitioned from rural to urban settings exhibit an average increase of 0.188 in height-for-age z-score (HAZ), compared to those born in rural settlements that remain rural. This improvement represents 14.4% of the advancement required to meet the WHO's average child height benchmark for the corresponding age group. Notably, urbanization's impact on child nutrition is not uniform across urban landscapes. Non-slum urban zones register the most beneficial effects, while slum areas sometimes manifest negative outcomes. Policy implications highlight the opportunity to leverage urbanization to improve child nutritional outcomes, but also emphasize the importance of addressing the disparities in urban areas through improved infrastructure, economic opportunities, education, and healthcare accessibilities. The second paper delves into the impact of spatial heterogeneity on machine learning-based poverty mapping, by employing spatial machine learning techniques and meticulously analyzing residuals across diverse locales. It aims to understand where the models may underperform. The findings indicate that variable relationships and model fit vary across different types of places. Extrapolation into unsurveyed areas is notably challenged by systematic overpredictions or underpredictions. In particular, overestimations of machine learning-based welfare estimates often occur in impoverished regions, rural areas, and single-sector dominated economies, while wealthier, urbanized, and diversified economies witness underestimations. Even as spatial machine learning models improve overall predictive accuracy, enhancements in traditionally underperforming areas are marginal. This underscores the necessity for more representative training datasets and better remotely-sensed proxies, especially for the poor and rural regions, in future research on machine learning-based poverty mapping. The third paper employs spatial analysis to examine the interplay between overlapping drought and heat stresses and multidimensional vulnerabilities of populations in East African countries, illuminating the diverse climate risks encountered by distinct regions and communities. The findings indicate that populations with lower wealth and multiple vulnerabilities often reside in areas most frequently and increasingly affected by compounded drought and heat stresses. Importantly, the critical vulnerabilities that require attention differ from place to place. This research contributes to the understanding of compound climate risks and emphasizes the necessity for tailored adaptation strategies that may include combinations of poverty alleviation, educational enhancements, health and nutrition improvements, and infrastructure development tailored to specific regional needs. The insights and methods from this study not only contribute to the academic discourse on climate risks but also serve as resources for policymakers and practitioners working towards climate resilience in similar settings globally.