Climate change has been identified as one the main public health challenges of this century and quantifying how different communities are affected is crucial to inform local adaptation strategies. While the number of empirical studies reporting the harmful health effects of climate-sensitive exposures has drastically increased in the past few years, methodological discussions and developments have mostly focused on time trends as a source of bias. However, other methodological challenges remain. One particular source of bias that received little attention in this area of research is related to spatial confounding. Furthermore, while most communities are exposed to climate-sensitive exposures such as extreme heat or ozone peaks, an important spatial heterogeneity regarding such exposures and related effect estimates may exist but approaches to handle such challenges remain underused or underdeveloped in this field. In the past decade, there has been growing interest in developing causal inference methods to answer various etiological questions such as mediation analyses to understand the mechanisms which through a given exposure may lead to a health outcome. Yet, little effort has been dedicated to incorporating spatial techniques when implementing such causal inference methods. Finally, an important mismatch can exist in regards to the scale at which environmental exposures and health data may be available which prevents an optimal identification of environmental-health patterns at a fine scale. Downscaling methods are quite common in many fields including climate sciences but have not been adapted yet to environmental health issues so empirical evidence can be available at the finest spatial resolution. In this dissertation we work toward precise analysis in this setting to advance spatial statistics in the context of climate and health research questions. First, we employ the combination of within-community matched design and Bayesian Spatial Hierarchical models to estimate at the zip code level the hospitalization burden of extreme heat events of varying definitions. Then we take a step into spatial causal inference to develop a procedure to estimate spatially varying estimates of mediation effects. And finally, we work toward a more ideal data setting through downscaling approaches coupled with machine learning algorithms, making the use of and adapting methods from Remote Sensing research to perform these tasks.