The invention providse an illumination device and display device. The illumination device includes a light guide plate, a light source, and a light modulation element. The light guide plate has convex portions extending in a direction parallel to a normal to a face opposed to the light source among side faces of the light guide plate, and the light source is configured of light source blocks. The light modulation element includes a pair of transparent substrates disposed separately and oppositely to each other, a plurality of first electrodes provided on a surface of one of the transparent substrates, and extending in a direction crossing an extending direction of the convex portions, a second electrode provided on a surface of the other transparent substrate, and a light modulation layer provided in a gap between the transparent substrates, and exhibiting a scattering property or a transparent property to light from the light source depending on magnitude of an electric field.