Two-dimensional (2D) semiconductor crystals with a thickness much smaller than their lateral dimensions are one of the key elements of modern microelectronic and optoelectronic. Recently, ultrathin semiconductor layers have been obtained or synthesized in a free-standing form, so that the ultrathin layers can be manipulated without their substrate1. We will present the synthesis of colloidal atomically flat, fluorescent chalcogenide nanoplatelets with a thickness that is controlled between 2 and 7 monolayers with atomic precision2. These nano-platelets can be extended laterally into nano-sheets up to the micron-scale3. As their spherical counter parts, the quantum dots, they can be grown into 2D core/shell structures which are the first demonstration of colloidal multiple quantum wells4. We will discuss the physical properties and the spectroscopy of this novel generation of 2D system that have quantum yield that can reach 80% at room temperature5, and radiative fluorescence lifetime as short as 300ps6. The auger recombination in these structures will be discussed and compared to the non-blinking core-thick shell spherical QDs we have recently synthesized and characterized7. I will present the first example of core/crown CdSe/CdS core/crown structures8. In the last part of the talk, we will show that these nano-platelets can be used for various applications ranging from light emitting diodes to bio-imaging.