Abstract: Understanding and predicting weather and climate extremes pose significant challenges due to the complex interactions among atmospheric variables, nonlinearity of underlying processes, and scarcity of data. Flexible statistical and machine learning approaches often fail to capture these complexities or lack interpretability, hindering practical applications. This talk will explore the evolution of interpretable machine learning methodologies applied to this domain, beginning with foundational work from the late 1990s, which introduced methods for visualizing functions computed by neural networks. The talk will trace subsequent advancements and applications, demonstrating how simple constraints on model architecture and parameters can lead to more interpretable and transparent models. Applications to predicting and analyzing weather and climate extremes — ranging from operational air quality forecasting, analysis of streamflow extremes, and projections of time-of-exceedance of global warming levels — will be presented, with an emphasis on how interpretability helped offer actionable insights to stakeholders and policy makers.