We discuss how geometry, optimization, and machine learning are key technologies that are revolutionizing the way we think about data and the way we transform data into actionable models and decisions. Specifically, we explain how complex data (e.g., text, molecules, time series, images/video, supply chain flows) can be represented as geometrical objects and how this facilitates the interpretation and extraction of useful information from data. We also discuss how extracted information can be mapped into decisions using optimization and machine learning models. We illustrate how to use these powerful math tools in innovative ways for analyzing complex datasets arising in molecular dynamics simulation, microscopy, chemical processes, and supply chains. Specifically, we show that these tools can help link the microstructure of soft gels to their rheological properties, can help analyze complex responses of liquid crystals from video data, and can help detect faults and optimize large-scale systems.