The nodal hypersurfaces of Laplacian eigenfunctions on a Riemannian manifold have fascinated mathematicians since Chladni's experiment. Courant gave an upper bound on the number of nodal domains, but no lower bound is known – it is not even true that the number of nodal domains must go to infinity with the frequency. The zero locus of polynomials is the central object of study in algebraic geometry. Real projective varieties are defined as the real zero locus of homogeneous polynomials. Understanding their topology is the first part of Hilbert's 16th problem, which remains enigmatic to this day. If one restricts attention to the number of connected components, the state of the art is only slightly better, since the optimal bounds are only known in low degree or dimension. These two examples are a motivation to study “random” polynomials or eigenfunctions of the Laplacian, and to study the topology of their zeroes from a probabilistic point of view. We will describe the approach of Nazarov and Sodin, and Gayet and Welschinger, in the case of Gaussian functions.