Intrinsically disordered proteins and peptides play key roles in biology, but the lack of defined structures and the high variability in sequence and conformational preferences has made targeting such systems challenging. We describe a general approach for designing proteins that bind intrinsically disordered protein regions in diverse extended conformations with side chains fitting into complementary binding pockets. We used the approach to design binders for 39 highly diverse unstructured targets and obtain designs with pM to 100 nM affinities in 34 cases, testing ∼22 designs per target (including polar targets). The designs function in cells and as detection reagents, and are specific for their intended targets in all-by-all binding experiments. Our approach is a major step towards a general solution to the intrinsically disordered protein and peptide recognition problem.