Congo red (CR) is a commonly used histological amyloid dye and a weak amyloid inhibitor. There is currently no experimentally available structure of CR bound to an amyloid fibril and the binding modes, and the mechanisms governing its inhibitory and optical properties are poorly understood. In this work, we present the first, to our knowledge, atomistically detailed picture of CR binding to protofibrils of the Alzheimer Aβ(9-40) peptide. We identify three major binding modes, with the primary mode residing in the grooves formed by the β-sheets, and observe a restriction of the torsional rotation of the CR molecule upon binding. Our simulations reveal a novel, to our knowledge, electrostatic steering mechanism that plays an important role in the initial recognition and binding of CR to the positively charged surface residues of the fibril. Our simulations provide new, to our knowledge, insights into the striking spectrophotometric and inhibitory properties of CR. In particular, we show that birefringence upon CR binding is due to the anisotropic orientation of the CR dipoles resulting from the spatial ordering of these molecules in the grooves along the fibril axis. The fluorescent enhancement of the bound CR, in turn, is associated with the torsional restriction of this molecule upon binding.