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We consider random matrices X with i.i.d. entries, and we analyseÌýitsÌýspectrum using Girko'sÌýformula. First, we show that the local spectralÌýstatistics at the edge is universal (the nonÌýHermitian analogue of theÌýcelebrated Tracy-Widom law). Second, we proveÌýthe GaussianÌýfluctuation ofÌýlinear eigenvalue statistics for generic test functions.ÌýThe proofs rely on aÌýcombination of three ingredients: (i) weakly correlatedÌýDyson Brownian motions, (ii) multiÌýresolvent local laws for theÌýHermitisation of X, (iii) rigorous supersymmetric (SUSY)Ìýapproach.