Reduced Order Modelling (ROM) found widespread application in numerical modelling at both industrial and academic level; its popularity is due primarily to the capability of those algorithms to retrieve the fundamental dynamics of a differential problem by reduction of the dimensionality of the parametric manifold that characterises the solution. In Computational Fluid Dynamics these methods are of particular importance since the parametric dependence of the models that are treated numerically is embedded in the engineering design process itself (e.g. shape optimisation). There is a particular class of problems however that pose a challenge to the effectiveness of ROM over the full-order simulations and those are the hyperbolic partial differential equations; there is in fact a sort of contradiction when it comes to time-dependent, parametric, transport equation and that is while at full order these models are easily handled, at least in CFD, with accurate, stable and robust methods, the low-rank representation is not straight-forward and difficult to retrieve with desired accuracy.