One of the simplest method to discretize the Boltzmann equation with respect to the velocity variable consists in approximating this dependence by a sum of Dirac measures. This yields respectively the discrete velocity method (DVM) when the abscissa are fixed, or the quadrature-based moment equations (which has many names in cluding QBMM and QMOM). Those methods are often used because of the simplicity of their construction. But they also have many drawbacks: they do not dissipate Boltzmann entropy, nor capture the equilibria (the Maxwellians) associated to it, they have singular solution (by construction) and yield weakly hyperbolic system (in the case of the quadrature-based moment equations), the inversion problem to compute the weigts and absissa is often ill-conditionned. In this talk, I will discuss about the entropic and hyperbolic structure of these systems. I will provide some modifications to retreive these desirable properties and study the resulting models.