The syntheses of strongly anisotropic nanocrystals with one dimension much smaller than the two others, such as nanoplatelets, are still greatly underdeveloped. Here, we demonstrate the formation of atomically flat quasi-two-dimensional colloidal CdSe, CdS and CdTe nanoplatelets with well-defined thicknesses ranging from 4 to 11 monolayers. These nanoplatelets have the electronic properties of two-dimensional quantum wells formed by molecular beam epitaxy, and their thickness-dependent absorption and emission spectra are described very well within an eight-band Pidgeon-Brown model. They present an extremely narrow emission spectrum with full-width at half-maximum less than 40 meV at room temperature. The radiative fluorescent lifetime measured in CdSe nanoplatelets decreases with temperature, reaching 1 ns at 6 K, two orders of magnitude less than for spherical CdSe nanoparticles. This makes the nanoplatelets the fastest colloidal fluorescent emitters and strongly suggests that they show a giant oscillator strength transition.