To fully understand the regulation of gene expression, it is critical to quantitatively define whether and how RNA-binding proteins (RBPs) discriminate between alternative binding sites in RNAs. Here, we describe new methods that measure protein binding to large numbers of RNA variants, and ways to analyse and interpret data obtained by these approaches, including affinity distributions and free energy landscapes. We discuss how the new methodologies and the associated concepts enable the development of inclusive, quantitative models for RNA-protein interactions that transcend the traditional binary classification of RBPs as either specific or nonspecific.