Two-dimensional II-VI semiconductor nanoplatelets (NPLs) gained increasing interest because of their unique electronic and optical properties, such as the Giant Oscillator Strength, strong electroabsorption response, low exciton-phonon interaction and high impact of dielectric confinement. The unusually small coupling to phonons makes NPLs potential candidates for materials with low dephasing rates, high lateral conductivity and control of both internal relaxation and energy transfer efficiencies. These platelets are of special importance since they combine large particle volumes with ultrastrong confinement. In this contribution we present a comprehensive study of the influence of dimensionality, size and shape on excitons in CdSe NPLs.   CdSe NPLs exhibit s-exciton state (GS) photoluminescence (PL), but also excited state (ES) luminescence. Calculations and time-integrated PL show a strong increase of the ES–GS energy spacing from about 18 to 38meV with increasing lateral quantization. Tuning the ES-GS energy separation allows to suppress or enhance the coupling to LO-phonons paving the way to a controlled switching of energy relaxation, charge transport or resonant energy transfer by lateral NPL size control. Thus CdSe NPLs are an attractive system allowing to control not only the exciton energy states by thickness (z-direction) but also with lateral size variation the LO-phonon coupling (x,y-direction) and this almost independently from each other. CdSe NPLs are an exemplary system of 2D-electronic states where the dielectric screening caused by the nanosheet environment has a major influence on the exciton energies and wavefunctions. The two-photon absorption cross sections of CdSe nano-platelets show ten times more efficient two-photon absorption than nanorods or dots per unit volume. The larger the particles' aspect ratio, the greater is the confinement related electronic contribution to the increased two-photon absorption. Both, electronic confinement and local field effects favor the platelets and make them unique two-photon absorbers with outstanding cross sections of up to 107 GM, the largest ever reported for (colloidal) semiconductor nanocrystals and ideally suited for two-photon imaging and non-linear opto-electronics. Finally we compare core-only NPLs and CdSe–CdTe and CdTe–CdSe type II hetero nanoplatelets [6] and observe a significant prolongation of the radiative lifetime in type II platelets by two orders in magnitude while the quantum yield is barely affected. We thus predict that the radiative lifetime can be tuned by a heterojunction via confinement and band offsets.