We study in detail the synthesis of CdTe nanoplatelets. Three populations of nanoplatelets with a thickness defined with atomic precision are obtained. We show that CdTe nanoplatelets can be extended laterally to obtain nanosheets with lateral dimensions in the micrometer range. We present the study of the reaction conditions for the formation of CdTe nanoplatelets and for their lateral extension. The reaction products are analyzed with optical spectroscopy, transmission electron microscopy, and small-angle X-ray scattering. We investigate the electro-optical properties of films formed with CdTe nanoplatelets, and we show that their current photoresponse is better than the one of comparable films formed with CdTe spherical nanocrystals.