The control and function of RNA are governed by the specificity of RNA binding proteins. Here, we describe a method for global unbiased analysis of RNA-protein interactions that uses in vitro selection, high-throughput sequencing, and sequence-specificity landscapes. The method yields affinities for a vast array of RNAs in a single experiment, including both low- and high-affinity sites. It is reproducible and accurate. Using this approach,we analyzed members of the PUF (Pumilio and FBF) family of eukaryotic mRNA regulators. Our data identify effects of a specific protein partner on PUF-RNA interactions, reveal subsets of target sites not previously detected, and demonstrate that designer PUF proteins can precisely alter specificity. The approach described here is, in principle, broadly applicable for analysis of any molecule that binds RNA, including proteins, nucleic acids, and small molecules.