The amount of data needed to adequately capture the behaviour of acoustical transmission systems is usually very large. This is not only due to the complex dynamical system behaviour but also the level of fidelity required for keeping up with the human auditory system. For this reason, it has been computationally infeasible to infer realistic state-space models of acoustical systems from data in the past. However, recently, the conjoined use of randomized matrix factorizations and classical system identification methods enabled the construction of large state-space realizations from high-dimensional measurement data. This paves the way for the employment of a plethora of sophisticated model order reduction techniques which in turn sheds new light onto many acoustical modelling challenges. This talk highlights specific challenges of data-driven modelling of acoustical systems. We consider the Eigensystem Realization Algorithm (ERA) and introduce several computational improvements that gear up this classic method for our use case. A validatory application of the method to room impulse response measurements is presented and several applicatory issues are discussed. Finally, an outlook on future research directions and ideas will be given.