In phase retrieval we want to recover an unknown signal ${boldsymbol x}inmathbb C^d$ from $n$ quadratic measurements of the form $y_i = |<{boldsymbol a}_i,{boldsymbol x}>|^2+w_i$ where ${boldsymbol a}_iin mathbb C^d$ are known sensing vectors and $w_i$ is measurement noise. We ask the following emph{weak recovery} question: what is the minimum number of measurements $n$ needed to produce an estimator $hat{boldsymbol x}({boldsymbol y})$ that is positively correlated with the signal $boldsymbol x$? We consider the case of Gaussian vectors ${boldsymbol a}_i$. We prove that -- in the high-dimensional limit -- a sharp phase transition takes place, and we locate the threshold in the regime of vanishingly small noise. For $nle d-o(d)$ no estimator can do significantly better than random and achieve a strictly positive correlation. For $nge d+o(d)$ a simple spectral estimator achieves a positive correlation. Surprisingly, numerical simulations with the same spectral estimator demonstrate promising performance with realistic sensing matrices. Spectral methods are used to initialize non-convex optimization algorithms in phase retrieval, and our approach can boost the performance in this setting as well. Our impossibility result is based on classical information-theory arguments. The spectral algorithm computes the leading eigenvector of a weighted empirical covariance matrix. We obtain a sharp characterization of the spectral properties of this random matrix using tools from free probability and generalizing a recent result by Lu and Li. Both the upper and lower bound generalize beyond phase retrieval to measurements $y_i$ produced according to a generalized linear model. As a byproduct of our analysis, we compare the threshold of the proposed spectral method with that of a message passing algorithm.