There are two efficient techniques to perform the $1/N$ expansion in matrix models : the method based on a CFT on a Riemann surface and the topological recursion. Both methods are defined uniquely in terms of the spectral curve of the matrix model. The CFT method uses the description of the matrix model as a conformal field theory on a Riemann surface, while the method of topological recursion is based on a recurrence equation for the observables representing symplectic invariants on the spectral curve. par We show that the two approaches give identical results and relate the corresponding diagram techniques.