In this talk, we introduce the spherical ensemble and more generally, the ratio of two independent random matrices with i.i.d. entries. We begin by reviewing some previous results for a single random matrix with i.i.d. entries. We then show that,  for any test function with finitely many logarithmic singularities, the linear statistics of the spherical ensemble converge to a Gaussian distribution, after a suitable normalization by 1/\sqrt{log n}. The limiting distribution depends only on the weights of singularities.  As an application, we obtain the finite-dimensional Gaussian convergence of the logarithm of the characteristic polynomial, normalization by 1/\sqrt{log n}. Moreover, we explicitly compute the variance and covariance without the 1/\sqrt{log n} normalization, showing that the field is log-correlated. All these results extend beyond spherical ensemble under a four moment matching condition. This is based on joint work with Djalil Chafaï and David García-Zelada.