Coherent diffractive imaging (CDI) is a novel technique for inspecting (crystalline and non-crystalline) matter from nanometric down to picometric resolution. It was used originally with X-rays and, more recently, with electrons (so-called electron diffractive imaging, or EDI). This chapter introduces basic concepts concerning CDI and addresses the different types of X-ray CDI experiments that have been conducted, namely plane wave CDI from isolated objects in forward scattering, focused-beam Fresnel CDI from isolated objects in forward scattering, Bragg CDI from nanocrystals, and keyhole CDI and ptychography from extended objects. A CDI experiment with a transmission electron microscope, alternatively named an EDI experiment, is also introduced.