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We describe several results obtained recently on stochastic non linear Schrödinger equations. We show that under suitable smoothness assumptions on the noise, the nonlinear Schrödinger perturbed by an additive or multiplicative noise is well posed under similar assumptions on the nonlinear term as in the deterministic theory. Then, we restrict our attention to the case of a focusing nonlinearity with critical or supercritical exponent. If the noise is additive, smooth in space and nondoi:10.1515/mcma.2001.7.1-2.55 fatcat:tur6n2nyzndoheeojrzg7aguyi