The eigenvalue statistics at the edge of the spectrum of large random matrices from the Gaussian unitary ensemble (GUE) are described by the Airy point process and the maximal eigenvalue is asymptotically Tracy-Widom distributed. In contrast, for the complex Ginibre ensemble (consisting of matrices with iid complex Gaussian entries), extreme eigenvalues behave like a Poisson process and the maximal modulus (or maximal real part) of the eigenvalues converges to a Gumbel-distributed random variable. In this talk, a family of ensembles interpolating between these models is considered, and we show how a non-trivial transition between Airy and Poisson statistics occurs for the eigenvalues near the edge of the spectrum.