Folding a linear chain of amino acids into a three-dimensional protein is a complex physical process that ultimately confers an impressive range of diverse functions. Although recent advances have driven significant progress in predicting three-dimensional protein structures from sequence, proteins are not static molecules. Rather, they exist as complex conformational ensembles defined by energy landscapes spanning the space of sequence and conditions. Quantitatively mapping the physical parameters that dictate these landscapes and protein stability is therefore critical to develop models that are capable of predicting how mutations alter function of proteins in disease and informing the design of proteins with desired functions. Here, we review the approaches that are used to quantify protein stability at a variety of scales, from returning multiple thermodynamic and kinetic measurements for a single protein sequence to yielding indirect insights into folding across a vast sequence space. The physical parameters derived from these approaches will provide a foundation for models that extend beyond the structural prediction to capture the complexity of conformational ensembles and, ultimately, their function.